Structured plane illumination microscopy

ABSTRACT

An apparatus includes a light source configured for generating a coherent light beam having a wavelength, λ, a light detector, and beam-forming optics configured for receiving the generated light beam and for generating a plurality of substantially parallel Bessel-like beams directed into a sample in a first direction. Each of the Bessel-like beams has a fixed phase relative to the other Bessel-like beams. Imaging optics are configured for receiving light from a position within the sample that is illuminated by the Bessel-like beams and for imaging the received light onto the detector. The imaging optics include a detection objective having an axis oriented in a second direction that is non-parallel to the first direction, where the detector is configured for detecting light received by the imaging optics. A processor configured to generate an image of the sample based on the detected light.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation-in-part of U.S. patent application Ser. No.13/160,492, filed Jun. 14, 2011, entitled “BESSEL BEAM PLANEILLUMINATION MICROSCOPE,” which, in turn, claims the priority of: U.S.Provisional Patent Application No. 61/354,532, filed Jun. 14, 2010,entitled “BESSEL BEAM PLANE ILLUMINATION MICROSCOPE”; U.S. ProvisionalPatent Application No. 61/386,342, filed Sep. 24, 2010, entitled “BESSELBEAM PLANE ILLUMINATION MICROSCOPE”; and U.S. Provisional PatentApplication No. 61/433,034, filed Jan. 14, 2011, entitled “BESSEL BEAMPLANE ILLUMINATION MICROSCOPE.” This application also claims priority tothis application also claims priority to U.S. Provisional PatentApplication No. 61/648,974, entitled “THREE-DIMENSIONAL IMAGING OFTHICKLY FLUORESCENT LIVING SPECIMENS BEYOND THE DIFFRACTION LIMIT,”filed May 18, 2012. The subject matter of each of these earlier filedapplications is hereby incorporated by reference.

TECHNICAL FIELD

This disclosure relates to microscopy and, in particular, to structuredplane illumination microscopy.

BACKGROUND

Several imaging technologies are commonly used to interrogate biologicalsystems. Widefield imaging floods the specimen with light, and collectslight from the entire specimen simultaneously, although high resolutioninformation is only obtained from that portion of the sample close tothe focal plane of the imaging objective lens. Confocal microscopy usesthe objective lens to focus light within the specimen, and a pinhole ina corresponding image plane to pass to the detector only that lightcollected in the vicinity of the focus. The resulting images exhibitless out-of-focus background information on thick samples than is thecase in widefield microscopy, but at the cost of slower speed, due tothe requirement to scan the focus across the entire plane of interest.

For biological imaging, a powerful imaging modality is fluorescence,since specific sub-cellular features of interest can be singled out forstudy by attaching fluorescent labels to one or more of theirconstituent proteins. Both widefield and confocal microscopy can takeadvantage of fluorescence contrast. One limitation of fluorescenceimaging, however, is that fluorescent molecules can be optically excitedfor only a limited period of time before they are permanentlyextinguished (i.e., “photobleach”). Not only does such bleaching limitthe amount of information that can be extracted from the specimen, itcan also contribute to photo-induced changes in specimen behavior,phototoxicity, or even cell death.

Unfortunately, both widefield and confocal microscopy excitefluorescence in every plane of the specimen, whereas the informationrich, high resolution content comes only from the vicinity of the focalplane. Thus, both widefield and confocal microscopy are very wasteful ofthe overall fluorescence budget and potentially quite damaging to livespecimens. A third approach, two photon fluorescence excitation (TPFE)microscopy, uses a nonlinear excitation process, proportional to thesquare of the incident light intensity, to restrict excitation toregions near the focus of the imaging objective. However, like confocalmicroscopy, TPFE requires scanning this focus to generate a completeimage. Furthermore, the high intensities required for TPFE can give riseto other, nonlinear mechanisms of photodamage in addition to thosepresent in the linear methods of widefield and confocal microscopy.

Thus, there is a need for the ability to: a) confine excitationpredominantly to the focal plane of imaging optics, to reducephotodamage and photobleaching, as well as to reduce out-of-focusbackground; b) use widefield detection, to obtain images rapidly; and c)use linear fluorescence excitation, to avoid nonlinear photodamage.

FIG. 1 is a schematic diagram of a light sheet microscopy (LSM) system100. As shown in FIG. 1, LSM uses a beam-forming lens 102, external toimaging optics, which includes an objective 104, to illuminate theportion of a specimen in the vicinity of the focal plane 106 of theobjective. In one implementation, the lens 102 that providesillumination or excitation light to the sample is a cylindrical lensthat focuses light in only one direction, thereby providing a beam oflight 108 that creates a sheet of light coincident with the objectivefocal plane 106. A detector 110 then records the signal generated acrossthe entire illuminated plane of the specimen. Because the entire planeis illuminated at once, images can be obtained very rapidly.

In another implementation, termed Digital Laser Scanned Light SheetMicroscopy (DSLM), the lens 102 can be a circularly symmetricmulti-element excitation lens (e.g., having a low numerical aperture(NA) objective) that corrects for optical aberrations (e.g., chromaticand spherical aberrations) that are prevalent in cylindrical lenses. Theillumination beam 108 of light then is focused in two directions to forma pencil beam of light coincident with the focal plane 106 of theimaging objective 104. The width of the pencil beam is proportional tothe 1/NA, whereas its length is proportional to 1/(NA)². Thus, by usingthe illumination lens 102 at sufficiently low NA (i.e., NA<<1), thepencil beam 108 of the excitation light can be made sufficiently long toencompass the entire length of the desired field of view (FOV). To coverthe other direction defining the lateral width of the FOV, the pencilbeam can be scanned across the focal plane (e.g., with a galvanometer,as in confocal microscopy) while the imaging detector 110 integrates thesignal that is collected by the detection optics 112 as the beam sweepsout the entire FOV.

A principal limitation of these implementations is that, due to thediffraction of light, there is a tradeoff between the XY extent of theillumination across the focal plane of the imaging objective, and thethickness of the illumination in the Z direction perpendicular to thisplane. In the coordinate system used in FIG. 1, the X direction is intothe page, the Y direction is in the direction of the illumination beam,and the Z direction is in the direction in which imaged light isreceived from the specimen.

FIG. 2 is a schematic diagram of a profile 200 of a focused beam oflight. As shown in FIG. 2, illumination light 202 of wavelength, λ, thatis focused to a minimum beam waist, 2w_(o), within the specimen willdiverge on either side of the focus, increasing in width by a factor of√{square root over (2)} in a distance of z_(R)=πw_(o) ²/λ, the so-calledRayleigh range. Table 1 shows specific values of the relationshipbetween the usable FOV, as defined by 2z_(R), and the minimum thickness2w_(o) of the illumination sheet, whether created by a cylindrical lens,or by scanning a pencil beam created by a low NA objective.

TABLE 1 2w_(o) (μm, for 2z_(R) (μm, for λ = 500 nm) λ = 500 nm) 0.2 0.060.4 0.25 0.6 0.57 0.8 1.00 1.0 1.57 2.0 6.28 5.0 39.3 10.0 157 20.0 628

From Table 1 it can be seen that, to cover FOVs larger than a fewmicrons (as would be required image even small single cells in theirentirety) the sheet thickness must be greater than the depth of focus ofthe imaging objective (typically, <1 micron). As a result, out-of-planephotobleaching and photodamage still remain (although less than inwidefield or confocal microscopy, provided that the sheet thickness isless than the specimen thickness). Furthermore, the background fromillumination outside the focal plane reduces contrast and introducesnoise which can hinder the detection of small, weakly emitting objects.Finally, with only a single image, the Z positions of objects within theimage cannot be determined to an accuracy better than the sheetthickness.

SUMMARY

In one general aspect, an apparatus includes a light source configuredfor generating a coherent light beam having a wavelength, λ, a lightdetector, and beam-forming optics configured for receiving the generatedlight beam and for generating a plurality of substantially parallelBessel-like beams directed into a sample in a first direction. Each ofthe Bessel-like beams has a fixed phase relative to the otherBessel-like beams. Imaging optics are configured for receiving lightfrom a position within the sample that is illuminated by the Bessel-likebeams and for imaging the received light onto the detector. The imagingoptics include a detection objective having an axis oriented in a seconddirection that is non-parallel to the first direction, where thedetector is configured for detecting light received by the imagingoptics. A processor configured to generate an image of the sample basedon the detected light.

In another general aspect, a method includes generating a coherent lightbeam having a wavelength, λ and generating from the coherent beam aplurality of substantially parallel Bessel-like beams directed into asample in a first direction. Each Bessel-like beam has a fixed phaserelative to the other Bessel-like beams. Light received from a positionwithin the sample that is illuminated by the Bessel-like beams isimaged, with imaging optics, onto a detector, where the imaging opticsinclude a detection objective having an axis oriented in a seconddirection that is non-parallel to the first direction. An image of thesample is generated based on the detected light.

In another general aspect, a method includes (a) providing activationradiation to a sample that includes phototransformable optical labels(“PTOLs”) to activate a statistically sampled subset of the PTOLs in thesample, wherein the PTOLs are distributed in at least a portion of thesample with a density greater than an inverse of the diffraction-limitedresolution volume (“DLRV”) of imaging optics. A sheet of excitationradiation is provided to the sample to excite at least some of theactivated PTOLs. The imaging optics detect radiation emitted fromactivated and excited PTOLs within the first subset of PTOLs, where theimaging optics include an objective lens having an axis along a seconddirection that is substantially perpendicular to the plane. Locationswithin the sample of the PTOLs from which radiation is detected withsuperresolution accuracy are determined. The activation radiation iscontrolled such that the density of activated PTOLs in the subset isless than the inverse of the (“DLRV”) of the imaging optics. Steps(a)-(e) are repeated to determine location of more PTOLs within thesample, and a sub-diffraction-limited image of the sample is generatedbased on the determined locations of the PTOLs.

The details of one or more implementations are set forth in theaccompanying drawings and the description below. Other features will beapparent from the description and drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a light sheet microscopy (LSM) system.

FIG. 2 is a schematic diagram of a profile of a focused beam of light.

FIG. 3 is a schematic diagram of a Bessel beam formed by an axicon.

FIG. 4 is a schematic diagram of a Bessel beam formed by an annularapodization mask.

FIG. 5 is a schematic diagram of a system for Bessel beam light sheetmicroscopy.

FIG. 6A is a plot of the intensity profile of a Bessel beam.

FIG. 6B shows a plot of the intensity profile of a conventional beam.

FIG. 7A is a plot of the intensity profile of a Bessel beam of FIG. 6Ain the directions transverse to the propagation direction of the beam.

FIG. 7B is a plot of the intensity profile of the conventional beam ofFIG. 6B in the directions transverse to the propagation direction of thebeam.

FIG. 8A is a plot of the intensity profile in the YZ plane of a Besselbeam generated from an annular mask having a thinner annulus in theannulus used to generate the intensity profile of the Bessel beam ofFIG. 6A.

FIG. 8B is a plot of the transverse intensity profile in the XZdirections for the beam of FIG. 8A.

FIG. 9A is a schematic diagram of another system for implementing Besselbeam light sheet microscopy.

FIG. 9B is a schematic diagram of another system for implementing Besselbeam light sheet microscopy.

FIG. 10 shows a number of transverse intensity profiles for differentBessel-like beams.

FIG. 11A shows the theoretical and experimental one-dimensionalintensity profile of a Bessel-like beam at the X=0 plane.

FIG. 11B shows an integrated intensity profile when the Bessel beam ofFIG. 11A is swept in the X direction.

FIG. 12A shows plots of the width of fluorescence excitation profiles ofa swept beam, where the beam that is swept is created from annuli thathave different thicknesses.

FIG. 12B shows plots of the axial intensity profile of the beam that isswept in the Z direction.

FIG. 13A is a schematic diagram of a surface of a detector having atwo-dimensional array of individual detector elements in the X-Y plane.

FIG. 13B is a schematic diagram of “combs” of multiple Bessel-likeexcitation beams that can be created in a given Z plane, where thespacing in the X direction between different beams is greater than thewidth of the fluorescence band generated by the side lobes of theexcitation beams.

FIG. 14A shows theoretical and experimental single-harmonic structuredillumination patterns that can be created with Bessel-like beams havinga maximum numerical aperture of 0.60 and the minimum vertical apertureof 0.58, which are created with 488 nm light.

FIG. 14B shows theoretical and experimental modulation transferfunctions in reciprocal space, which correspond to the point spreadfunctions shown in the two left-most columns of FIG. 14A.

FIG. 15A shows theoretical and experimental higher-order harmonicstructured illumination patterns that can be created with Bessel-likebeams having a maximum numerical aperture of 0.60 and the minimumvertical aperture of 0.58, which are created with 488 nm light.

FIG. 15B shows theoretical and experimental modulation transferfunctions (MTFs) in reciprocal space, which correspond to the pointspread functions shown in the two left-most columns of FIG. 15A.

FIG. 16 shows a system with a galvanometer-type mirror placed at a planethat is conjugate to the detection objective between the detectionobjective and the detector.

FIG. 17A shows two overlapping structured patterns. FIG. 17B shows areciprocal space representation of one of the patterns of FIG. 17A. FIG.17C shows shows a reciprocal space representation of the other patternof FIG. 17A. FIG. 17D shows an observable region of a reciprocal spacerepresentation of specimen structure shifted from the reciprocal spaceorigin. FIG. 17E shows observable regions of reciprocal spacerepresentations of specimen structure shifted from the reciprocal spaceorigin, where the different representations correspond to differentorientations and/or phases of a structured pattern overlayed with thespecimen structure.

FIG. 18A is a schematic diagram of a system for producing an array ofBessel-like beams in a sample.

FIG. 18B is a view of an array of Bessel-like beams.

FIG. 18C is another view of the array of Bessel-like beams shown in FIG.18B.

FIG. 18 D is a plot of the relative intensity of light produced by thearray of Bessel-like beams shown in FIG. 18B and FIG. 18C along a linein which the beams lie.

FIG. 19 is a schematic diagram of another system for producing an arrayof Bessel-like beams in a sample.

FIG. 20 is a flowchart of a process of determining a pattern to apply toa binary spatial light modulator, which will produce a coherentstructured light sheet having a low height in the Z direction over asufficient length in the Y direction to image samples of interest.

FIG. 21 shows a series of graphical illustrations of the process of FIG.20. FIG. 21A illustrates a cross-sectional profile in the X-Z plane of aBessel like beam propagating in the Y direction. FIG. 21B illustratesthe electric field, in the X-Z plane, of a structured light sheet formedby coherent sum of a linear, periodic array of Bessel-like beams thatpropagate in the Y direction. FIG. 21C illustrates the electric field,in the XZ plane, of the structured light sheet of FIG. 21B after aGaussian envelope function has been applied to the field of the lightsheet to bound the light sheet in the Z direction. FIG. 21D illustratesthe pattern of phase shifts applied to individual pixels of a binaryspatial light modulator to generate the field shown in FIG. 21C. FIG.21E illustrates the cross-sectional point spread function, in the X-Zplane, of the structured plane of excitation radiation that is producedin the sample by the coherent array of Bessel-like beams, which aregenerated by the pattern on the spatial light modulator shown in FIG.21D. FIG. 21F illustrates the excitation beam intensity that is producedin the sample when the array of Bessel-like beams is swept or ditheredin the X direction.

FIG. 22 shows a series of graphical illustrations of the process shownin FIG. 20. FIG. 22A illustrates a cross-sectional profile in the X-Zplane of a Bessel like beam propagating in the Y direction. FIG. 22Billustrates the electric field, in the X-Z plane, of a structured lightsheet formed by a coherent sum of a linear, periodic array ofBessel-like beams that propagate in the Y direction. FIG. 22Cillustrates the electric field, in the XZ plane, of the structured lightsheet of FIG. 22B after a Gaussian envelope function has been applied tothe field of the light sheet to bound the light sheet in the Zdirection. FIG. 22D illustrates the pattern of phase shifts applied toindividual pixels of a binary spatial light modulator to generate thefield shown in FIG. 22C. FIG. 22E illustrates the cross-sectional pointspread function, in the X-Z plane, of the structured plane of excitationradiation that is produced in the sample by the coherent array ofBessel-like beams, which are generated by the pattern on the spatiallight modulator shown in FIG. 22D. FIG. 22F illustrates the modulationtransfer function, which corresponds to the point spread functions shownin FIG. 22E.

FIG. 23 is a schematic diagram of the intensities of different modes ofexcitation radiation that is provided to the sample. FIG. 23A is across-sectional in the X-Z plane of a Bessel-like beam propagating inthe Y direction. FIG. 23B is a schematic diagram of the time-averagedintensities in the X-Z plane that results from sweeping the Bessel-likebeam of FIG. 23A in the X direction. FIG. 23C is a cross-sectional inthe X-Z plane of a superposition of incoherent Bessel-like beamspropagating in the Y direction, such as would occur if the singleBessel-like beam in FIG. 23A were moved in discrete steps. FIG. 23D is aschematic diagram in the X-Z plane of the time-averaged intensity thatresults from moving multiple instances of the array of Bessel-like beamsof FIG. 23C in small increments in the X direction and integrating theresulting signal on a camera. FIG. 23E is a cross-section in the X-Zplane of a superposition of coherent Bessel-like beams propagating inthe Y direction. FIG. 23F is a schematic diagram of the time-averagedintensity in the X-Z plane that results from sweeping or dithering thearray of Bessel-like beams of FIG. 23E.

FIG. 24 is a flowchart of a process of determining a pattern to apply toa binary spatial light modulator, which will produce an optical latticewithin the sample, where the optical lattice can be used as a coherentstructured light sheet having a relatively low thickness extent in the Zdirection over a sufficient length in the Y direction to image samplesof interest.

FIG. 25 shows a series of graphical illustrations of the process shownin FIG. 24, when the process is used to generate an optical lattice ofstructured excitation radiation that is swept in the X direction togenerate a plane of excitation illumination. FIG. 25A illustrates across-sectional profile in the X-Z plane of an ideal two-dimensionalfundamental hexagonal lattice that is oriented in the Z direction. FIG.25B illustrates the electric field, in the XZ plane, of the opticallattice of FIG. 25A after a Gaussian envelope function has been appliedto the optical lattice to bound the lattice in the Z direction. FIG. 25Cillustrates the pattern of phase shifts applied to individual pixels ofa binary spatial light modulator to generate the field shown in FIG.25B. FIG. 25D illustrates the cross-sectional point spread function, inthe X-Z plane, of the structured plane of excitation radiation that isproduced in the sample by the optical lattice, which is generated by thepattern on the spatial light modulator shown in FIG. 25C, and thenfiltered by an annular apodization mask that limits the maximum NA ofthe excitation to 0.55 and the minimum NA of the excitation to 0.44.FIG. 25E illustrates the excitation beam intensity that is produced inthe sample when the bound optical lattice pattern in FIG. 25D is sweptor dithered in the X direction. Higher intensities are shown by whiterregions.

FIG. 26 illustrates the light patterns of at a plurality of locationsalong the beam path shown in FIG. 19 when the pattern shown in FIG. 25Cis used on the SLM of FIG. 19. FIG. 26A a schematic diagram of thepattern of phase shifts applied to individual pixels of a binary spatiallight modulator to generate the field shown in FIG. 25B. FIG. 26B aschematic diagram of the intensity of light that impinges on anapodization mask downstream from a SLM. FIG. 26C a schematic diagram ofthe transmission function of an apodization mask. FIG. 26D a schematicdiagram of the intensity of light immediately after the apodizationmask. FIG. 26E is a schematic diagram of an optical lattice that resultsat the sample when then the pattern of the light that exists just afterthe apodization mask is focused by an excitation objective to the focalplane within the sample. FIG. 26F is a schematic diagram of theintensity patter that results when the optical lattice of FIG. 26E isswept or dithered in the X direction.

FIG. 27 shows a series of graphical illustrations of the process, whenthe processes used to generate an optical lattice of structuredexcitation radiation that is translated in the X direction in discretesteps to generate images of the sample using superresolution, structuredillumination techniques. FIG. 27A is a schematic diagram of across-sectional profile in the X-Z plane of a two-dimensionalfundamental hexagonal lattice that is oriented in the Z direction. FIG.27B is a schematic diagram of the electric field, in the XZ plane, ofthe optical lattice of FIG. 27A after a Gaussian envelope function hasbeen applied to the optical lattice to bound the lattice in the Zdirection. FIG. 27C is a schematic diagram of the pattern of phaseshifts applied to individual pixels of a binary spatial light modulatorto generate the field shown in FIG. 27B. FIG. 27D is a schematic diagramof the cross-sectional point spread function, in the X-Z plane, of thestructured plane of excitation radiation that is produced in the sampleby the optical lattice, which is generated by the pattern on the spatiallight modulator shown in FIG. 27C, and then filtered by an annularapodization mask that limits the maximum NA of the excitation to 0.60and the minimum NA of the excitation to 0.54. FIG. 27E is a schematicdiagram of the modulation transfer function, in reciprocal space, whichcorresponds to the intensity pattern shown FIG. 27D.

FIG. 28 illustrates the light patterns at a plurality of locations alongthe beam path shown in FIG. 19 when the pattern shown in FIG. 27C isused on the SLM of FIG. 19. FIG. 28A is a schematic diagram of thepattern of phase shifts applied to individual pixels of a binary spatiallight modulator to generate the field shown in FIG. 27B. FIG. 28B is aschematic diagram of the intensity of light that impinges on theapodization mask downstream from the SLM when the SLM includes thepattern of FIG. 28A. FIG. 28C is a schematic diagram of the transmissionfunction of the apodization mask. FIG. 28D is a schematic diagram of theintensity of light immediately after the apodization mask. FIG. 28E is aschematic diagram of an optical lattice that results from the pattern ofthe light shown in FIG. 28D being focused by an excitation objective tothe focal plane within a sample. FIG. 28F is a schematic diagram of themodulation transfer function for this lattice shown in FIG. 28E.

FIG. 29 is a plurality of graphs illustrating the effect of the Z axisbounding of the optical lattice on the light sheets produced in thesample. FIG. 29A is a schematic diagram of the intensity of the opticallattice to which a wide, or weak, envelope function is applied. FIG. 29Bis a schematic diagram of the intensity profiles of a light sheetcreated by sweeping or dithering the lattice of FIG. 29A. FIG. 29C is aschematic diagram of the intensity of the optical lattice to which amedium-wide envelope function is applied. FIG. 29D is a schematicdiagram of the intensity profiles of a light sheet created by sweepingor dithering the lattice of FIG. 29C. FIG. 29E is a schematic diagram ofthe intensity of the optical lattice to which a medium-narrow envelopefunction is applied to the ideal optical lattice pattern. FIG. 29F is aschematic diagram of the intensity profiles of a light sheet created bysweeping or dithering the lattice of FIG. 29E. FIG. 29G is a schematicdiagram of the intensity of the optical lattice to which a narrow, orstrong, envelope function is applied to the ideal optical latticepattern. FIG. 29H is a schematic diagram of the intensity profiles of alight sheet created by sweeping or dithering the lattice of FIG. 29G.

FIG. 30 is a schematic diagram illustrating a PTOLs (e.g., a fluorescentmolecule) stimulated by excitation radiation from a ground state into anexcited state that emits a portion of the energy of the excited stateinto a fluorescence radiation photon.

FIG. 31 is a schematic diagram illustration excitation radiation thatcan excite an isolated emitter into an excited state.

FIG. 32 is a schematic diagram illustrating how when weak intensityactivation radiation bathes closely spaced PTOLs a small,statistically-sampled fraction of all the PTOLs that absorbs theactivation radiation can be converted into a state that can be excitedby excitation radiation.

FIG. 33 is a schematic diagram illustrating how multiple sub-diffractiveresolution images in two spatial dimensions, x and y, of individualPTOLs in a sample can be generated, and then the multiple images can becombined to generate a sub-diffraction limited resolution image of anx-y plane of the sample.

FIG. 34 is a flow chart of a process for creating an image of a samplecontaining multiple relatively densely-located PTOLs.

FIG. 35 is a schematic view of a system that can be used to implementthe techniques described herein.

DETAILED DESCRIPTION

This description discloses microscopy and imaging apparatus, systems,methods and techniques, which enable a light sheet or pencil beam tohave a length that can be decoupled from its thickness, thus allowingthe illumination of large fields of view (e.g., tens or even hundreds ofmicrons) across a plane having a thickness on the order of, or smallerthan, the depth of focus of the imaging objective by using illuminationbeams having a cross-sectional field distribution that is similar to aBessel function. Such illumination beams can be known as Bessel beams.Such beams are created by focusing light, not in a continuum ofazimuthal directions across a cone, as is customary, but rather at asingle azimuthal angle or range of azimuthal angles with respect to theaxis of the focusing element. Bessel beams can overcome the limitationsof the diffraction relationship shown in FIG. 2, because therelationship shown in FIG. 2 is only valid for lenses (cylindrical orobjectives) that are uniformly illuminated.

FIG. 3 is a schematic diagram of a Bessel beam formed by an axicon 300.The axicon 300 is a conical optical element, which, when illuminated byan incoming plane wave 302 having an approximately-Gaussian intensitydistribution in directions transverse to the beam axis, can form aBessel beam 304 in a beam that exits the axicon.

FIG. 4 is a schematic diagram of a Bessel beam 400 formed by an annularapodization mask 402, where the annular mask 402 is illuminated tocreate a thin annulus of light at the back focal plane of a conventionallens 404. The mask 402 is separated from the lens 404 by the focallength, f. An angle, θ, can be defined as the inverse tangent of halfthe distance, d, from the center of the annular ring to a point withinthe ring divided by the focal length, where d_(o) can be used to denotethe minimum diameter of the annular ring. Ideally, in either case shownby FIG. 3 or by FIG. 4, the axial wavevectors k_(z) of all raysconverging to the focus are the same, and hence there is no variation ofthe beam along this direction. In practice, the finite diameter of theaxicon 300, or the finite width, Δd, of the annular ring in theapodization mask 402 restricts the Bessel beam to a finite length. Theoptical system of the annular apodization mask 402 and the lens 404 canbe characterized by a minimum and maximum numerical aperture, where themaximum numerical aperture is proportional to d_(o)+Δd, and the minimumnumerical aperture is proportional to d_(o). In other implementations,different optical elements, other than an axicon or an apodization mask,can be used to create an annulus of light. For example, a binary phasemask or a programmable spatial light modulator can be used to create theannulus of light.

FIG. 5 is a schematic diagram of a system 500 for Bessel beam lightsheet microscopy. A light source 502 emits a light beam 504 that strikesan annular apodization mask 506. An annulus of excitation light 508illuminates the back focal plane of microscope objective 510 to createan elongated Bessel beam 512 of light in a sample 514. By scanning thisbeam in a plane 516 transverse to the axis of the Bessel beam 512 andcoincident with the focal plane of a detection objective 504 whilesimultaneously integrating the collected signal 518 with a camera 520located at a corresponding image plane of imaging optics 522, an imageis obtained from a much thinner slice within the sample than is the casewhen either conventional light sheet microscopy or DSLM is used.

How much thinner the sheet of excitation light can be with Bessel beamillumination than with conventional light sheet microscopy or DSLM canbe seen from a comparison of FIG. 6A, which shows a plot of theintensity profile of a Bessel beam, and FIG. 6B, which shows a plot ofthe intensity profile of a conventional beam. In the plots of FIGS. 5and 6, Y is along the axis of the propagation direction of the beam, Xis the direction of the excitation polarization (when linearly polarizedlight is used), and Z is along the axis of detection optics objective522 and is orthogonal to X and Y. FIG. 7A is a plot of the intensityprofile of a Bessel beam of FIG. 6A in the directions transverse to thepropagation direction of the beam, and FIG. 7B is a plot of the Gaussianintensity profile of the conventional beam of FIG. 7A in the directionstransverse to the propagation direction of the beam.

As seen in FIG. 6A, annular illumination across a small range of angles(θ=43 to 45 degrees) results in a Bessel-like beam approximately 50wavelengths λ long in the Y direction, or roughly the same lengthobtained by conventional illumination using a plane wave having aGaussian transverse intensity profile that is focused by a lens into anillumination beam having a cone half-angle of 12 degrees, as seen inFIG. 6b . However, the thickness of the Bessel beam is much narrowerthan the thickness of the conventional beam, yielding a much thinnersheet of excitation when scanned across a plane.

Furthermore, even longer Bessel-like beams can be made withoutcompromising their cross-sectional width simply by restricting theannular illumination over an even smaller range of angles. FIG. 8A is aplot of intensity profile in the YZ directions of a Bessel beamgenerated from an annular mask having a thinner annulus than is used togenerate the intensity profile of the Bessel-like beam of FIG. 6A, andFIG. 8B is a plot of the transverse intensity profile for the beam inthe XZ directions. As shown in FIG. 8A, annular illumination across asmall range of angles (θ=44 to 45 degrees) results in the YZ intensityprofile of the Bessel-like beam shown in FIG. 8A, where the Bessel-likebeam has a length of approximately 100 wavelengths in the Y direction.However, the transverse intensity profile of the longer Bessel beam isrelatively unchanged compared with shorter Bessel beam, as can be seenfrom a comparison of FIG. 7A and FIG. 8B, and the thickness of the beamis not significantly greater than the thickness of the beam whoseintensity profile is shown in FIG. 6A. In contrast, with conventionalillumination the usual approach of lengthening the beam by reducing theNA results in an unavoidably larger diffraction limited cross-section,roughly in accordance with Table 1.

FIG. 9A is a schematic diagram of another system 900 for implementingBessel beam light sheet microscopy. Collimated light 901, such as alaser beam having a Gaussian intensity profile, is reflected from firstgalvanometer-type mirror 902 and then imaged by relay lens pair 903 and904 onto a second galvanometer-type mirror 905 positioned at a pointoptically conjugate to the first galvanometer-type mirror 902. A secondlens pair 906 and 907 then relays the light to annular apodization mask908 conjugate with the second galvanometer-type mirror 905. The annularlight beam transmitted through this mask 908 is then relayed by a thirdlens pair 910 and 911 onto a conjugate plane coincident with the backfocal plane of excitation objective 912. Finally, the annular light isfocused by objective 912 to form a Bessel-like beam 913 that is used toprovide excitation light to a specimen.

The rotational axis of galvanometer mirror 902 is positioned such thattilting this galvanometer-type mirror 902 causes the Bessel-like beam913 to sweep across the focal plane of detection objective 915 (i.e., inthe X direction), whose axis is orthogonal to (or whose axis has anorthogonal component to) the axis of the excitation objective 912. Thesignal light 914 can be directed by detection optics, including thedetection objective 915, to a detection camera 917. Thegalvanometers-type mirrors 902, 905 can provide sweep rates of up toabout 2 kHz, and with resonant galvanometer-type mirrors (e.g.,Electro-Optical Products Corp, model SC-30) sweep rates can exceed 30kHz. Extremely high frame rate imaging is then possible when the systemis used in conjunction with a high frame rate detection camera (e.g.,500 frames/sec with an Andor iXon+DU-860 EMCCD, or >20,000 frames/secwith a Photron Fastcam SA-1 CMOS camera coupled to a Hamamatsu C10880-03image intensifier/image booster).

The rotational axis of the galvanometer mirror 905 is positioned suchthat tilting of this mirror causes Bessel-like beam 913 to translatealong the axis of detection objective 915. By doing so, different planeswithin a specimen can be accessed by the Bessel beam, and a threedimensional (3D) image of the specimen can be constructed, with muchhigher axial resolution than in conventional light sheet microscopy, dueto the much narrower sheet of excitation afforded by Bessel-likeexcitation. In order to image each plane in focus, either detectionobjective 915 must be moved synchronously with the motion of the Besselbeam 913 imparted by the tilt of galvanometer-type mirror 905 (such aswith a piezoelectric transducer (e.g., Physik Instrumente P-726)), orelse the effective plane of focus of the detection objective 915 must bealtered, such as by using a second objective to create a perfect imageof the sample. Of course, if 3D image stacks are not desired, the secondgalvanometer 905 and relay lenses 906 and 907 can be removed from thesystem shown in FIG. 9A, and the first galvanometer 902 and relay lenses903 and 904 can be repositioned so that the apodization mask 908 is at aconjugate plane relative to galvanometer-type mirror 902. Anacousto-optical tunable filter (AOTF) 918 can be used to block allexcitation light from reaching the specimen when desired.

The system in FIG. 9A is typically quite wasteful of the energy in lightbeam 901, because most of this light is blocked by apodization mask 908.If greater efficiency is desired, a diffractive optical element such asa binary phase mask or spatial light modulator and a collimating lenscan be used to create an approximately annular light beam prior to moreexact definition of this beam and removal of higher diffractive ordersby the apodization mask 908.

In another implementation, shown in FIG. 9B, signal light 914 receivedby detection objective 915 can be transmitted through relay lenses 920,922 and reflected off a galvanometer-type mirror 924 and thentransmitted through relay lenses 926 and 928 and focused by a tube lens930 onto a detector 932. An aperture mask (e.g., an adjustable slit) 934can be placed at a focal plane of lens 926, and the when the maskdefines a slit the width of the slit 934 can be selected to block signallight from positions in the sample corresponding to side lobes of theBessel-like beam illumination light, while passing signal light frompositions in the sample corresponding to the central peak of theBessel-like beam illumination light. The galvanometer-type mirror 924can be rotated in conjunction with galvanometer-type mirror 902, so thatwhen the Bessel-like beam is scanned in the X direction within thesample signal light from different positions within the sample passesthrough the slit 934.

Bessel-like beams include excitation intensity in rings other than thecentral excitation maximum, which are evident in FIGS. 7A and 8B, andsubstantial energy resides in the side lobes of a Bessel-like beam.Indeed, for an ideal Bessel beam of infinite extent, each side lobecontains energy equal to that in the central peak. Also, for an idealBessel beam, the ratio of the Rayleigh length of the beam to the minimumwaist size of the beam is infinite. FIG. 10 shows a number of transverseintensity profiles for different Bessel-like beams. In FIG. 10, thefirst column shows theoretical two-dimensional intensity plots in the XZplane, the second column shows experimental intensity plots in the thirdcolumn shows a one-dimensional intensity profile at the X=0 plane.Different rows in FIG. 10 correspond to Bessel-like beams that arecreated using different annular apodization masks. Each row indicatesthe maximum and minimum numerical aperture of the annular ring of themask. In the first row, the maximum numerical aperture is 0.80, and theminimum numerical aperture is 0.76. In the second row, the maximumnumerical aperture is 0.60, and the minimum numerical aperture is 0.58.In a third row, the maximum numerical aperture is 0.53 and the minimumnumerical aperture is 0.51. In the fourth row the maximum numericalaperture is 0.40, and the minimum numerical aperture is 0.38. In thefifth row, the maximum numerical aperture is 0.20, and the minimumnumerical aperture is 0.18.

Because of the intensity in the side lobes, the integrated fluorescenceexcitation profile after the beam is swept in the X direction exhibitsbroad tails, as shown in FIG. 11. FIG. 11A shows the theoretical andexperimental intensity profile in the Z direction of a Bessel-like beam,when the center of the beam is fixed at the X=0 and Z=0 plane, whereexperimental values are shown by dots and theoretical values are shownby solid lines. The intensity profile shown in FIG. 11A isrepresentative of a Bessel-like beam formed from an annular apodizationmask that generates an annulus of 488 nm light at a rear pupil of anexcitation objective, where the annulus has a maximum numerical apertureof 0.60 and a minimum numerical aperture of 0.58. When this Bessel-likebeam is swept in the X direction to create a sheet of excitation lightcentered on the Z=0 plane, integrated fluorescence excitation profileshown in FIG. 11B results because of the side lobes in the beam. Thus,the side lobes of the Bessel beam can contribute out-of-focus backgroundfluorescence and premature photobleaching of the sample. A number oftechniques can be used to mitigate the effect of these lobes.

Choosing a thicker annulus in the annular mask 506 suppresses thesetails, but it does so at the expense of the length of the beam, as thebeam becomes more Gaussian and less Bessel-like in character. Thiseffect can be seen in FIG. 12A and FIG. 12B. FIG. 12A shows plots of thewidth of fluorescence excitation profiles of beams swept in the Xdirection in the Z=0 plane, where the beams that are swept are createdfrom annuli that have different thicknesses. FIG. 12B shows plots of theaxial intensity profiles (i.e., in the Y direction) of the beams thatare swept. For each of the beams whose intensity profiles are plotted inFIG. 12A and FIG. 12B, the maximum numerical aperture is 0.60. A beamwith an intensity profile 1202 has a minimum numerical aperture equal to0.58. A beam with an intensity profile 1204 has a minimum numericalaperture equal to 0.56. A beam with an intensity profile 1206 has aminimum numerical aperture people equal to 0.52. The beam with anintensity profile 1208 has a minimum numerical aperture equal to 0.45. Abeam with an intensity profile 1210 has a minimum numerical apertureequal to 0.30. A beam with an intensity profile 1212 as a minimumnumerical aperture equal to 0.00, i.e., it is equivalent to the Gaussianbeam that fully illuminates a circular aperture.

Thus, as can be seen from a comparison of the plot FIG. 12A and FIG.12B, a trade-off exists between minimizing the deleterious effects ofthe side lobes of the beam and maximizing the axial length of the fieldof view of the beam. Therefore, by selecting an annulus having athickness that achieves a length of the field of view that is justsufficient to cover a region of interest in a specimen, but that is notsubstantially longer than the region of interest, the deleteriouseffects of the side lobes can be minimized. Therefore, the system 500shown in FIG. 5, can include a plurality of different apodization masks506 in which the thickness of the open annular region varies, and aparticular one of the apodization masks 506 can be selected to image aregion of the specimen 514, where the selected mask is chosen such thatthe length of the field of view of beam just covers the region ofinterest. When referring to FIG. 4, the different apodization masks canhave open regions with different widths, Δd.

Thus, a comparison of the plots in FIG. 12A and FIG. 12B shows theprofiles of the beam changing from a profile that best approximates thatof a lowest order (J₀) Bessel function (plot 1202) to a Gaussian profile(1212). This comparison indicates that the deleterious effect of theside lobes can be reduced by using a beam having a profile that is notsubstantially similar to that of a Bessel function, at the expense ofhaving a beam with a shorter axial length. This means that it can beadvantageous to select a beam profile having a minimum length necessaryto create the desired image, so that the effect of the side lobes of thebeam, which create background haze and photobleaching, can be minimized.Thus, the beam that may be selected may not have a profile thatapproximates that of a Bessel function, but the beam also may not have aprofile of a Gaussian beam, because the annular mask 506 blocks theportion of the incoming light 504 on the axis of the excitationobjective 510 such that the k_(z)=0 of the beam 516 are removed. Inparticular, in one implementation, the selected beam can have a ratio ofa Rayleigh length, z_(R) to a minimum beam waist, w_(o), of more than2πw_(o)/λ and less than 100πw_(o)/λ. In another implementation, theselected beam can have a non-zero ratio of a minimum numerical apertureto a maximum numerical aperture of less than 0.95. In anotherimplementation, the selected beam can have a non-zero ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.9. Inanother implementation, the selected beam can have a ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.95 andgreater than 0.80. In another implementation, the selected beam can havea non-zero ratio of a minimum numerical aperture to a maximum numericalaperture of less than 0.9. In another implementation, the selected beamcan have a ratio of a minimum numerical aperture to a maximum numericalaperture of less than 0.95 and greater than 0.80. In anotherimplementation, the selected beam can have a ratio of energy in a firstside lobe of the beam to energy in the central lobe of the beam of lessthan 0.5.

The length of the beam 516 that is necessary to image a specimen can bereduced by tilting a cover slip that supports the specimen with respectto the direction of the incoming beam 516. For example, if a specimenthat resides on a cover slip is 5 μm thick in the direction normal tothe cover slip and has lateral dimensions of 50 μm×50 μm then, if thecover slip lies in the Z=0 plane, the beam 516 would have to be 50 μmlong to span the specimen. However, by tilting the plane of the coverslip at a 45° angle to the direction of the incoming beam 516, then thebeam would only need to be 5 μm×√2 long to span the sample. Thus, byplacing a thin specimen on a cover slip and tilting the cover slip withrespect to the direction of the incoming beam, a shorter length beam canbe used, which has the advantage of reducing the effect of backgroundhaze and photobleaching due to side lobes of the beam. To image thespecimen on a tilted cover slip, the beam 516 can be scanned in the Xdirection by tilting the galvanometer-type mirror 902, and can bescanned in the Z direction either by introducing a third galvanometer(not shown) and a third pair of relay lenses (not shown) into the system900 shown in FIG. 9A to scan the beam 516 in the Z direction or bytranslating the Z position of the specimen, e.g., via a piezoelectrictransducer (not shown and FIG. 9A) coupled to the cover slide thatsupports the specimen. This mode of operation in which a specimen on acover slip is imaged when the cover slip is tilted (e.g., at an anglebetween 10 and 80 degrees) with respect to the direction of the incomingillumination beam can be used to image thin (e.g., less than 10 μmthick) specimens, such as individual cells that are mounted or culturedon to the cover slip.

Another approach to isolate the central peak fluorescence from thatgenerated in the side lobes is to exclude the latter via confocalfiltering with a virtual slit. When the detector includes a plurality ofindividual detector elements, only those elements of the detector whichan image the portion of the sample that is illuminated by the centrallobe of the illumination beam can be activated to record informationthat is used to generate an image, while the individual detectorelements upon which an image of the portion of the sample that isilluminated by side lobes of the illumination beam are not activated,such that they do not record information that is used to generate animage.

For example, FIG. 13A is a schematic diagram of a surface of a detectorhaving a two-dimensional array of individual detector elements in the XYplane. When the center of the central lobe of the excitation beam islocated at X=0 and side lobes are located at X>0 and X<0, then thedetector elements 1302 onto which fluorescence or detection light isfocused from the X=0 position within the specimen at the focal plane ofthe detection objective 915 (or detector elements corresponding to thesmallest absolute value of X for a particular Y position) can beactivated to record information, while neighboring detector elementscorresponding to higher absolute values of X for the particular Yposition can be un-activated such that they do not record informationthat is used to generate an image. As shown in FIG. 13A, detectorelements 1302 located on the detector surface at positions thatcorrespond most closely with fluorescence light from X=0 positionswithin the specimen can be activated to record information, whileneighboring detector elements 1304, 1306 are unactivated, so they do notrecord fluorescence light from positions within the sample that are notilluminated by the central portion of the excitation beam.

FIG. 13B is a schematic diagram of “combs” of multiple Bessel-likeexcitation beams that can be created in a given Z plane. A comb of beamscan be created by inserting a diffractive optical element (DOE, notshown) in the beam path between the light source and thegalvanometer-type mirrors 902, 905, where the DOE diffracts a pluralityof beams at different angles from the DOE, which end up being parallelto and spatially shifted from each other within the specimen. In thespecimen at the focal plane of the detection objective, the spacing inthe X direction between different beams of the comb is greater than thewidth of the fluorescence band generated by the side lobes of the beams.This allows information to be recorded simultaneously from rows ofindividual detector elements corresponding to the centers of thedifferent beams of the comb, without the side lobes of neighboring beamsinterfering with the recorded signal for a particular beam.

For example, as shown in FIG. 13B, a comb of beams that illuminate aplane of a specimen 1308 can include the beams A1, B1, C1, D1, and E1,where the beams are separated by distances great enough so that sidelobes of one beam in the comb do not overlap with a central portion of aneighboring beam. In this manner, multiple “stripes” of an image can besimultaneously recorded. This process is then repeated, with additionalimages collected as the comb of Bessel-like illumination beams istranslated in discrete steps having a width that corresponds to thespacing in the X direction between individual detector elements untilall “stripes” of the final image have been recorded. For example, thebeams can be moved to new positions of A2, B2, C2, D2, and E2, where thespacing between the positions A1 and A2, the spacing between positionsB1 and B2, etc. corresponds to the spacing between neighboringindividual detector elements in the detector. Thus, fluorescence lightfrom the beam position C1 could be detected at a detector element 1302,while fluorescence light from the beam position C2 can be detected atindividual detector elements 1304. The image is then digitallyconstructed from the information in all of the different stripes of theimage. An acousto-optical tunable filter (AOTF) 918 can be used to blockall excitation light from reaching the specimen between steps.

Another technique to reduce the influence of the side lobes and toreduce the Z-axis size of the field of view from which detection lightis received is to employ structured illumination (SI) based opticalsectioning. In a widefield microscopy implementation of SI, a periodicexcitation pattern can be projected through an epi-illuminationobjective to the focal plane of the objective, and three images of asample, I_(n) (n=1, 2, 3), are acquired as the pattern is translated insteps of ⅓ of the period of the pattern. Since the observable amplitudeof the pattern decreases as it becomes increasingly out of focus (i.e.,in a direction perpendicular to the focal plane), combining the imagesaccording to:

$\begin{matrix}{I_{final} = \left| {\sum\limits_{n = 1}^{N}\;{I_{n}{\exp\left( {2\pi\;{in}\text{/}N} \right)}}} \right|} & (1)\end{matrix}$with N=3 removes the weakly modulated out-of-focus component and retainsthe strongly modulated information near the focal plane. In equation(1), I is an intensity at a point in the image, and n is an index valueindicating an image from which I_(n) is taken. Equation (1) is but oneexample of a linear combination of the individual images that willremove the weakly modulated out-of-focus component and retain thestrongly modulated information near the focal plane.

To use SI using a Bessel-like beam with a wavelength, λ, thatilluminates a thin plane of a specimen and where light is emitted in adirection perpendicular to (or in a direction with a componentperpendicular to the illumination plane, the beam may not be sweptcontinuously, but rather can be moved in discrete steps to create apattern of illumination light from which an image I_(n) can begenerated. When the stepping period is larger than or approximatelyequal to the minimum period of λ/2NA_(Bessel) ^(max) required to producea resolvable grating, but smaller than or approximately equal toλ/NA_(Bessel) ^(max), the imposed pattern of illumination light containsa single harmonic, as required for the three-image, three-phase SIalgorithm.

Thus, referring to FIG. 9A, the Bessel-like beam 913 can be moved acrossthe X direction in discrete steps having a period greater than orapproximately equal to λ/2NA_(Bessel) ^(max) and less than orapproximately equal to λ/NA_(Bessel) ^(max) by controlling the positionof the galvanometer-type mirror 902, and detection light can be receivedand signals corresponding to the detected light can be recorded by thedetector 917 when the beam 913 is in each of the positions. While thegalvanometer-type mirror is being moved from one position to the nextposition, the illumination light can be blocked from reaching the sampleby the AOTF. In this manner, an image I₁ can be generated from thedetected light that is received when the illumination beam 913 is ateach of its different positions. Then, additional images, I₂ . . .I_(N), can be created by again stepping the beam 913 across the specimenin the X direction to create a pattern of illumination light, but withthe patterns spatially shifted from the position of the first pattern by(i−1)/N of the period of the pattern, for i=2 to N. A final image of thespecimen then can be constructed from the recorded signals through theuse of equation (1).

FIG. 14A shows theoretical and experimental structured illuminationpatterns that can be created with a 488 nm light Bessel-like beam havinga maximum numerical aperture of 0.60 and the minimum numerical apertureof 0.58, that is moved across the X direction in discrete steps. Theleftmost column of figures shows theoretical patterns of the pointspread functions of the excitation light produced by stepping the beamacross the X direction in discrete steps. The middle column showsexperimentally-measured patterns, and the third column showsone-dimensional intensity patterns for the Z=0 plane (top figure) andthe X=0 (bottom figure) plane, respectively, in each of the three rowsof FIG. 14A. In the first row of FIG. 14A, the period the pattern (i.e.,the spacing between successive positions of the center of theBessel-like being as the beam is stepped in the X direction) is 0.45 μm.In the second row, the period of the pattern is 0.60 μm. In the thirdrow the period of the pattern is 0.80 μm. FIG. 14B shows theoretical andexperimental modulation transfer functions (MTFs) in reciprocal space,which correspond to the point spread functions shown in the twoleft-most columns of FIG. 14A. All of the MTFs are normalized to themaximum frequency, k_(max)=2NA_(exc) ^(max)/λ set by Abbe's Law, withNA_(exc) ^(max)=0.8 for the excitation objective.

As described above, rather than stepping a single beam across the Xdirection, a comb of multiple Bessel-like beams, which are spaced bymore than the width of the fringes of the beams in the comb, can be usedto illuminate the specimen simultaneously, and then the comb of beamscan be stepped in the X direction using the step size described above,so that different stripes of the specimen can be imaged in parallel andthen an image of the specimen can be constructed from the multiplestripes.

The excellent optical sectioning of the single harmonic SI mode resultsfrom the removal of the k_(x)=0 band in the excitation modulationtransfer function (MTF) under application of Eq. (1). However, due tothe energy in the Bessel side lobes, considerably more spectral energyexists in this band than in the two side bands, so that its removalproves wasteful of the photon budget and reduces the SNR of the finalimages substantially. Somewhat more energy can be transferred to theside bands using single harmonic excitation having a period far beyondthe λ/2NA_(detect) ^(max) Abbe limit, but at the expense ofproportionally poorer optical sectioning capability.

An alternative that can better retain both signal and axial resolutionis to create a multi-harmonic excitation pattern by stepping the beam ata fundamental period larger than λ/NA_(Bessel) ^(max), as seen in FIG.15A, which shows theoretical and experimental higher-order harmonicstructured illumination patterns that can be created with Bessel-likebeams having a maximum numerical aperture of 0.60 and the minimumvertical aperture of 0.58, which are created with 488 nm light. Tocreate a single SI image with a pattern having H harmonics, Eq. (1) isagain used, except with N≥H+2 images, each with the pattern phaseshifted by 2π/N relative to its neighbors.

FIG. 15B shows theoretical and experimental modulation transferfunctions (MTFs) in reciprocal space, which correspond to the pointspread functions shown in the two left-most columns of FIG. 15A. Asshown in FIG. 15B, with increasing H, more side bands are generated inthe MTF that contain a greater combined fraction of the total spectralenergy relative to the k_(x)=0 band, thus yielding highersignal-to-noise (SNR) images. Due to the greater weighting of thesesidebands to lower k_(z), axial resolution (i.e., along the axis of thedetection objective 915) of this multi-harmonic SI mode is slightly less(0.29 μm FWHM for N=9 phases) than in the single harmonic case, yetimages of fixed and living cells still exhibit isotropic 3D resolution,albeit at the cost of more data frames required per image plane, andthus lower speed.

In addition to this speed penalty, both single-harmonic andmulti-harmonic SI modes still generate some excitation beyond the focalplane, and are thus not optimally efficient in their use of the photonbudget. Both these issues can be addressed using two-photon excitation(TPE), which suppresses the Bessel side lobes sufficiently such that athin light sheet can be obtained even with a continuously swept beam. Asa result, high axial resolution and minimal out-of-focus excitation isachieved in fixed and living cells with only a single image per plane.Some additional improvement is also possible with TPE-SI, but the fasterTPE sheet mode can be preferred for live cell imaging. The benefits ofTPE are not limited to structured illumination excitation of thespecimen, but are beneficial during other modes of Bessel-like beamplane illumination of the specimen to reduce out of focus excitation andphoto damage by the illumination beam. Other forms of non-linearexcitation with a Bessel like beam, such as coherent anti-Stokes Ramanscattering (CARS), can also reap similar benefits.

Thus, the improved confinement of the excitation light to the vicinityof the focal plane of the detection objective made possible by Besselbeam plane illumination leads to improved resolution in the axialdirection (i.e., in the direction along the axis of the detectionobjective) and reduced photobleaching and phototoxicity, therebyenabling extended observations of living cells with isotropic resolutionat high volumetric frame rates. For example, extended imaging of theendoplasmic reticulum in a live human osteosarcoma cell (U2OS cell line)in the linear multi-harmonic SI mode was performed. Despite the factthat over three-hundred image slices were required to construct each 3Dimage stack, the dynamics of the ER could be followed over 45 minutes ata rate of 1 stack/min with axial resolution of ˜0.3 μm.

Even longer duration observations were found to be possible in the TPEsheet mode. For example, portions of three consecutive image stacks froma series of one hundred such stacks showed the evolution of numerousfilopodia on the apical surface of a HeLa cell transfected withmEmerald/Lifeact. Significantly, the imaging speeds achievable in thismode (51.4 image planes/sec, 6 sec stack interval) enable even complex,rapid 3D cellular processes to be visualized with sufficient timeresolution. This is further underscored by consecutive images of theretrograde flow of membrane ruffles formed at the leading edge of atransformed African green monkey kidney cell (COS-7 cell line,transfected with mEmerald/c-src). Such ruffles can surround and engulfextracellular fluid to create large intracellular vacuoles, a processknown as macropinocytosis, which was directly demonstrated using thetechniques described herein. The visualization of these processes infour dimensional spatiotemporal detail (0.12×0.12×0.15 μm×12.3 sec stackinterval) across 15 minutes cannot currently be achieved with otherfluorescence microscopy techniques.

For sufficiently bright samples, the pixel rate of EMCCD cameras becomesa limiting factor. To achieve even higher imaging speeds in such cases,a scientific CMOS camera (125 MHz, Hamamatsu Orca Flash 2.8) can beused. To exploit the full speed of the camera, a third galvanometer-typemirror that can be tilted can be placed at a plane conjugate to the rearpupil of the detection objective and used to tile several image planesacross the width of the detector, which were then are read out inparallel.

FIG. 16 shows a system 1600 with a mirror placed at a plane that isconjugate to the detection objective between the detection objective andthe detector. In the system 1600, detection light collected by detectionobjective 1602 can be focused by a tube lens 1604 to form an image atthe plane of an adjustable slit 1606. The image cropped by theadjustable slit 1606 is reimaged by relay lenses 1608 onto a high-speeddetection camera 1610. A galvanometer-type mirror 1612 is placed theplane between the relay lenses 1608 that is conjugate to the back focalplane of the detection objective 1612. By changing the angle ofgalvanometer-type mirror, multiple images can be exposed across thesurface of the detection camera 1610 and then read out in parallel toexploit the full speed of the detection camera 1610.

With this configuration, the 3D dynamics of chromatid separation inearly anaphase could be studied in the TPE sheet mode at rates of 1volume/sec. Significantly, even at these imaging rates, the excitationdid not arrest mitosis. Moreover, the intracellular trafficking ofvesicles in a COS-7 cell could be observed over the course of 7000frames acquired in a single plane at 191 frames/sec.

Three-dimensional live cell imaging can be performed with Bessel-likebeans with the use of fluorescent proteins to highlight selectedportions of a specimen. A key aspect of fluorescent proteins (FPs) isthat their spectral diversity permits investigation of the dynamicinteractions between multiple proteins in the same living cell. Forexample, after transfection with mEmerald/MAP4 and tdTomato/H2B,microtubules in a pair of U2OS cells surrounding their respectivenuclei, were imaged in the linear, nine-phase multi-harmonic SI mode.Nevertheless, although many vectors are available for linear imaging,the need for N frames of different phase per image plane can limits theuse of SI with Bessel-like beams to processes which evolve on a scalethat matches the time required to collect frames at the desired spatialresolution. Of course, this limitation does not apply for fixed cells,where the linear SI mode is preferred, due to its superior axialresolution and the availability of a wider array of fluorescent dyes aswell as FPs for protein specific labeling. For example, three-colorisotropic 3D imaging of the actin cytoskeleton of an LLC-PK1 cellstained with Alexa Fluor 568 phalloidin, the nuclear envelope taggedwith mEmerald/lamin B1, and nuclear histones tagged with mNeptune/H2Bwas performed.

For imaging multiple proteins exhibiting faster dynamics, the TPE sheetmode can be used. However, this presents its own challenges: orange/redFPs such as tdTomato and mCherry do not have the same TPE brightness andphotostability of green FPs such as EGFP or mEmerald and require asecond expensive ultrafast light source, since the time required toretune and realign a single source is prohibitive for live cell imaging.Fortunately, the 3D isotropic resolution of the Bessel TPE sheet modepermits multiple proteins tagged with the same FP to be imagedsimultaneously, as long as they are known a priori to be spatiallysegregated. For example, the fragmentation of the Golgi apparatusbetween metaphase (t=0 min) and anaphase (t=10 min) was observed, asidentified by chromosome morphology (green), and the re-constitution ofthe Golgi (t=20 min) around the daughter nuclei in telophase (t=40 min).

As described herein, Bessel beam plane illumination microscopytechniques offer 3D isotropic resolution down to ˜0.3 μm, imaging speedsof nearly 200 planes/sec, and the ability, in TPE mode, to acquirehundreds of 3D data volumes from single living cells encompassing tensof thousands of image frames. Nevertheless, additional improvements arepossible. First, substantially greater light collection making stillbetter use of the photon budget is obtained by using a detectionobjective with a numerical aperture of 1.0 or greater. Althoughmechanical constraints would thereby force the use of an excitationobjective with a numerical aperture of less than 0.8 thus lead to asomewhat anisotropic point spread function (PSF), the volumetricresolution would remain similar, since the slight loss of axialresolution would be offset by the corresponding transverse gain.

As noted above, SI using the algorithm in Eq. (1) is also photoninefficient, as it achieves high axial resolution by removingsubstantial spectral energy that resides in the k_(x)=0 band of the MTF.An alternative would be to use the algorithms of 3D superresolution SI,which assign the sample spatial frequencies down-modulated by all bandsof the excitation to their appropriate positions in an expandedfrequency space. By doing so, shorter exposure times and fewer phasesare needed to record images of acceptable SNR, making linear Bessel SI amore viable option for high speed multicolor imaging. In addition,resolution can be extended to the sum of the excitation and detectionMTF supports in each direction—an argument in favor of using threemutually orthogonal objectives. Indeed, the marriage of Bessel beamplane illumination and 3D superresolution SI permits the latter to beapplied to thicker, more densely fluorescent specimens than theconventional widefield approach, while more efficiently using the photonbudget.

Superresolution SI can be performed by extending the structuredillumination techniques described above with respect to FIG. 14 and FIG.15. By illuminating the sample with a structured illumination pattern,normally inaccessible high-resolution information in an image of asample can be made accessible in the form of Moiré fringes. A series ofsuch images can be processed to extract this high-frequency informationand to generate reconstruction of the image with improved resolutioncompared to the diffraction limited resolution.

The concept of super resolution SI exploits the fact that when twopatterns are superimposed multiplicatively a beat pattern will appear inthe product of the two images, as seen in FIG. 17A. In the case ofBessel-like beam plane illumination microscopy, one of the patterns canbe the unknown sample structure, for example, the unknown spatialdistribution of regions of the sample that receive illumination lightand that emit signal light—and the other pattern can be the purposelystructured pattern of excitation light that is written in the form ofparallel Bessel-like beams. Because the amount of signal light emittedfrom a point in the sample is proportional to the product of the localexcitation light intensity and the relevant structure of the sample, theobserved signal light image that is detected by the detector will showthe beat pattern of the overlap of the two underlying patterns. Becausethe beat pattern can be coarser than those of the underlying patterns,and because the illumination pattern of the Bessel-like beams is known,the information in the beat pattern can be used to determine thenormally unresolvable high-resolution information about the sample.

The patterns shown in FIG. 17A can be Fourier transformed intoreciprocal space. For example, the Fourier transform of the structure ofa sample that is imaged by an a convention widefield optical system isconstrained by the Abbe resolution limit would be represented by acircle having a radius of 2NA/λ, as shown in FIG. 17B, where the lowresolution components of the sample are close to the origin, and thehigh-resolution components are close to the edge of the circle. TheFourier transform of a 2D illumination pattern that consists of asinusoidal variation in the illumination light in one dimension andhaving a period equal to the diffraction limit of the optical system hasthree non-zero points that lie on the circle shown in FIG. 17C. Onepoint resides at the origin and the other two points are offset from theorigin in a direction defined by the orientation of the illuminationpattern by distances proportional to the inverse of the spatial periodof the pattern. When the specimen is illuminated by structuredillumination, the resulting beat pattern between the specimen structureand the illumination structure represents information that has changedposition in reciprocal space, such that the observable region of thesample in physical space then contains new high-frequency informationrepresented by the two regions and FIG. 17D that are offset from theorigin. For example, the regions of the offset circles in FIG. 17 D thatfall outside the central circle represent new information that is notaccessible with a conventional eidefield technique. When a sequence ofsuch images is obtained using structured excitation radiation that isoriented in different directions multiple circles that lie outside thecentral circle are produced, as shown in FIG. 17E. From this pluralityof images, information can be recovered from an area that can be twicethe size of the normally observable region, to increase the lateralresolution by up to a factor of two is compared with widefieldtechniques.

In an implementation using a structured illumination pattern ofBessel-like beams, as explained above with respect to FIG. 14 and FIG.15, N images can be recorded with the spatial phase of the illuminationpattern between each image shifted by Λ/N in the X direction, where Λ isthe spatial period of the pattern and N is the number of harmonics inreciprocal space. Then, a Fourier transform can be performed on each ofthe N images, and the reciprocal space images can moved to their truepositions in reciprocal space, combined through a weighted-average inreciprocal space, and then the weight-averaged reciprocal space imagecan be re-transformed to real space to provide an image of the sample.In this manner, a superresolution image of the sample can be obtained,where the resolution of the image in both the X and Z directions can beenhanced over the Abbe diffraction limited resolution. The resolutionenhancement in the X direction can be up to a factor of two when the NAof the structured excitation and the NA of the detection are the same.However, the excitation lens NA is usually lower than that of thedetection lens, so the extension beyond the Abbe limit is usually lessthan a factor of two but more than a factor of one. In the Z direction,the resolution improvement can be better than a factor of two, since thetransverse Z resolution of the excitation can exceed the transverse Zresolution of the detection.

In another implementation, more than one excitation objective can beused to provide a structured illumination pattern to the sample, wherethe different excitation objectives can be oriented in differentdirections, so that super resolution of the sample can be obtained inthe directions transverse to the Bessel-like beams of each of theorientation patterns. For example, a first excitation objective can beoriented with its axis along the Y direction (as described above) andcan illuminate the sample with an illumination pattern of Bessel-likebeams that provides a superresolution image of the sample in the X and Zdirections, and a second excitation objective can be oriented with itsaxis along the X direction and can illuminate the sample with anillumination pattern of Bessel-like beams that provides asuperresolution image of the sample in the Y and Z directions. Thesuperresolution information that can be derived from illuminationpatterns from the different excitation objectives can be combined toyield extended resolution in all three directions.

In another implementation, highly inclined, objective-coupled sheetillumination has been used to image single molecules in thicker regionsof the cell where autofluorescence and out-of-focus excitation would beotherwise prohibitive under widefield illumination. With the thinnerlight sheets possible with Bessel beam plane illumination, only in-focusmolecules would be excited, while out-of-focus ones would not beprematurely bleached. As such, it would be well suited to live cell 3Dparticle tracking and fixed cell photoactivated localization microscopy.

At the other extreme, the TPE sheet mode may be equally well suited tothe imaging of large, multicellular specimens, since it combines theself-reconstructing property of Bessel beams with the improved depthpenetration in scattering media characteristic of TPE. In addition tolarge scale 3D anatomical mapping with isotropic resolution, at highframe rates it might be fruitfully applied to the in vivo imaging ofactivity in populations of neurons. When the sample is excited withtwo-photon excitation radiation, additional spatial frequencies areintroduced to images generated from detected light that is emitted fromthe sample, and the additional spatial frequencies can provideadditional information that may be exploited to enhance the resolutionof a final image of the sample generated through the super resolutionstructured illumination techniques described herein. The infraredexcitation light used in TPE can penetrate tissue with reducedscattering and aberration, and the out-of-focus emission from the sidelobes of the excitation beam can be suppressed. Similarly, thesuppression of the side lobes confines the TPE excitation radiation moreclosely to the Z=0 plane permitting substantial axial resolutionimprovement when applied to SR-SIM.

FIG. 18A is a schematic diagram of a system 1800 for generating andproviding an array of Bessel-like excitation beams to a sample, similarto the comb of beams show in FIG. 13B, and for imaging the light emittedfrom the sample due to interaction between the Bessel-like beams and thesample.

As shown in FIG. 18A, a light source 1802 (e.g., a laser) can producecoherent, collimated light such as a beam having a Gaussian intensityprofile, which can be reflected from first galvanometer-type mirror1804. The mirror 1804 can be controlled by a fast motor 1806 that isused to rotate the mirror and steer the beam in the X direction. Afterthe beam is reflected from the mirror 1804, it is imaged by relay lenspair 1808 and 1810 onto a second galvanometer-type mirror 1812positioned at a point optically conjugate to the first galvanometer-typemirror 1804. The mirror 1812 can be controlled by a fast motor 1814 thatis used to rotate the mirror and steer the beam in the Z direction.

A second lens pair 1816 and 1818 then can relay the light to adiffractive optical element (DOE) 1824 located just in front of anannular apodization mask (AM) 1822 that is conjugate with the secondgalvanometer-type mirror 1812. The DOE 1820 can be, for example, aholographic diffractive optical element, that creates, in the far fieldfrom the DOE, a fan of Gaussian beams. In some implementations, the DOEcan create a fan of seven beams. The apodization mask 1822, located justafter the DOE 1820, can be used in combination with the DOE to generatean array of Bessel-like beams in the sample 1840.

The annular light beams transmitted through the AM 1822 are relayed by athird lens pair 1826 and 1828 onto a conjugate plane coincident with theback focal plane of excitation objective 1830. Finally, the annularlight beams are focused by the objective 1830 to form a fan ofBessel-like beam s that are used to provide excitation light to thesample 1840. The sample 1840 can be placed in an enclosed sample chamber1832 that can be filled with aqueous media and that can be temperaturecontrolled. Signal light emitted from the sample can be collimated by adetection objective 1834 and focused by a tube lens 1836 onto a positionsensitive detector 1838. The signal light emitted from the sample can begenerated through a non-linear signal generation process. For example,in one implementation, the signal light may be generated through atwo-photon process, such that the signal light has a wavelength that isone half the wavelength of the excitation light of the Bessel-likebeams.

FIGS. 18B and 18C, are example diagrams showing an array ofsubstantially parallel Bessel-like beams produced by the system 1800.FIG. 18B shows the array of beams in the X-Y plane, and FIG. 18C showsthe array of beams in the X-Z plane, although FIG. 18C shows only fiveof the seven Bessel-like beams. In one implementation, a diffractiveoptical element that produces seven beams in combination with the otherbeam-forming optics of system 1800, including the apodization mask 1822and the excitation objective 1830, can create the array of sevenBessel-like beams shown in FIGS. 18B and 18C. As shown in FIGS. 18B and18C, the beams, for particular parameters and configurations of thebeam-forming optics of system 1800, including the dimensions of theapodization mask, the numerical aperture of the excitation objective1830, etc. the Bessel-like beams that are produced in the sample canextend over a length of approximately 10 μm, and can have central lobeswith diameters on the order of 1 μm. FIG. 18D is a schematic figureshowing a relative intensity plots of five of the seven Bessel-likebeams along the X-axis at the Y=0, Z=0 plane. As shown in FIG. 18D, inthis implementation, the intensity profiles of neighboring Bessel-likebeams do not substantially overlap. Nevertheless, use of the array of Nnon-overlapping beams spreads the excitation energy over N beams insteadof concentrating the energy in just one beam, and, therefore, the sampleis subject to less damage. In addition an array having a plurality ofbeams can be stepped across the sample to create an incoherentstructured illumination pattern over a given field of view faster thanone beam can be stepped.

The rotational axis of galvanometer mirror 1804 can be positioned suchthat tilting this galvanometer-type mirror 1804 causes the array ofBessel-like beams to sweep across the focal plane of detection objective1834 (i.e., in the X direction), whose axis is orthogonal to (or whoseaxis has an orthogonal component to) the axis of the excitationobjective 1830. Thus, through control of the galvanometer-type mirror1804, the array of Bessel-like beams can be swept in the X direction toproduce a thin sheet of light in a plane.

The signal light emitted from the sample 1840 can be directed bydetection optics, including the detection objective 1834, to a detector1838. The galvanometers-type mirrors 1804, 1812 can provide sweep ratesof up to about 2 kHz, and with resonant galvanometer-type mirrors (e.g.,Electro-Optical Products Corp, model SC-30) sweep rates can exceed 30kHz. Extremely high frame rate imaging is then possible when the systemis used in conjunction with a high frame rate detection camera.

The rotational axis of the galvanometer mirror 1812 can be positionedsuch that tilting of this mirror causes the array of Bessel-like beamsto translate along the Z axis of detection objective 1834. By doing so,different planes within a specimen can be accessed by the Bessel beam,and a three dimensional (3D) image of the specimen can be constructed,with much higher axial resolution than in conventional light sheetmicroscopy, due to the much narrower sheet of excitation afforded byarray of Bessel-like excitation. In order to image each plane in focus,either detection objective 1834 must be moved synchronously with themotion of the array of Bessel-like beams imparted by the tilt ofgalvanometer-type mirror 1812 (such as with a piezoelectric transducer),or else the effective plane of focus of the detection objective 1834must be altered, such as by using a second objective to create a perfectimage of the sample. In another implementation, the excitation plane andthe detection plane can remain fixed and the sample can be moved throughthe planes, for example, by using a piezoelectric transducer to move thesample through the beam to cover different z planes. For relatively flatsamples, this allows the use of a shorter Bessel-like beams in theY-direction with less energy in the side-lobes.

The plurality of Bessel-like beams can lie in a plane within the sampleand can be equally spaced from neighboring beams, such that theplurality of beams form a pattern in the plane having a spatial period,A. The array of beams can be scanned in a direction perpendicular totheir propagation direction (e.g., in the X direction). In someimplementations, the array of beams can be scanned in a series ofdiscrete steps. For example, the array of beams can be scanned from itsoriginal position in N−1 discrete steps, where N is an integer, and thesteps can have a length of (N−1)·Λ/N. Images of the sample can berecorded based on light emitted from the sample when the array ofBessel-like beams is in each of the N different positions within thesample (i.e., in the original position and in the N−1 scannedpositions). Then, a final image of the sample can be generated through alinear combination of the N individual images of the sample. Forexample, the linear combination of the different images can be createdaccording to

$I_{final} = \left| {\sum\limits_{n = 1}^{N}\;{I_{n}{\exp\left( {2\pi\;{in}\text{/}N} \right)}}} \middle| . \right.$where I_(final) is an intensity of the final image at a particularposition within the sample, n is an index variable corresponding to thedifferent individual images that are generated, and In is an intensityof the particular position within the sample in the nth individualimage.

In some implementations, the array of the Bessel-like beams can bespatially dithered (i.e., rapidly changed in a periodic manner) at adither frequency back and forth in the plane of the array of beams. Forexample, the galvanometer-type mirror 1804 can be tilted back and forthto dither the spatial position of the array of Bessel-like beams. Thearray of Bessel-like beams can be spatially dithered over a distancegreater than or approximately equal to the spatial period, Λ, of thepattern of the array of Bessel-like beams. While dithering the array,the Bessel-like beams can be moved in the plane at the array (e.g.,along the X axis) at a substantially constant rate, so that thetime-averaged intensity of light in the plane of the array issubstantially constant. When the inverse of the dither frequency isgreater than the integration time of the detector 1838, the excitationlight provided by the array of Bessel-like beams in the sample canappear to the detector as a uniform sheet of excitation light.

The system in FIG. 18A is typically quite wasteful of the energy inlight beam 1801, because most of this light is blocked by apodizationmask 1808. If greater efficiency is desired, a diffractive opticalelement such as a binary phase mask or spatial light modulator and acollimating lens can be used to create an approximately annular lightbeam prior to more exact definition of this beam and removal of higherdiffractive orders by the apodization mask 1808.

The different, substantially parallel Bessel-like beams that areproduced from the light of the light source and the beam-forming opticsshown in FIG. 18A, can be created from a single source of coherentlight, and the beam-forming optics can be held in stable positions, suchthat fixed phase relationships exist between the different substantiallyparallel Bessel-like beams in the sample. In some implementations, forexample, in the implementation shown in FIGS. 18B, 18C, and 18D, thedifferent Bessel-like beams can be spaced apart from the other with thespacing that is great enough so that the light from neighboring Besselbeams does not interact substantially.

Structured Illumination Microscopy with an Array of Bessel-Like Beams

Another technique to reduce the influence of the side lobes and toimprove the Z-axis resolution of images obtained of a sample is toemploy structured illumination using a coherent array of Bessel-likebeams that are provided simultaneously to the sample, such thatinterference between the beams of the coherent array improves the Z-axisconfinement of the plane of structured illumination that is used toprovide excitation radiation to the sample. One way to imagine thecreation of such a structured illumination plane is to think of theplane being created by different beams that are spaced apart from theirneighboring beams by distances small enough for neighboring beams tooverlap and interfere with each other. For example, in someimplementations neighboring Bessel-like beams can be spaced by distancesthat are less than or comparable to a diameter of a first side lobe ofthe Bessel-like beams. Interference between the beams then creates astructured light sheet of high modulation depth within the desired Z=0plane, improving the performance in optically sectioned orsuperresolution structured plane illumination. In addition, destructiveinterference between the side lobes outside the Z=0 plane reduces theout-of focus excitation from the side lobes, reducing phototoxicity anddecreasing the thickness of the light sheet created by sweeping ordithering the structured light sheet.

FIG. 19 is a schematic diagram of another system 1900 for producing anarray of Bessel-like beams in a sample. As shown in FIG. 19, the lightbeam from the light source 1902 can be spatially expanded in the Xdirection by a pair of cylindrical lenses 1904A, 1904B and can bespatially reduced in the Z direction by a pair of cylindrical lenses1906A, 1906B to produce a beam having an intensity profile that is widein the X direction and narrow in the Z direction.

The beam can pass through a beam splitter 1908 half-wave plate 1910 andthen impinge on a wavefront modulating element (WME) 1912 thatindependently modulates individual portions of the entire wavefront. Theinsertion of the half-wave plate 1910 in the beam path can make the WME1912 operate as a phase modulator of portions of the beam that strikethe WME. In some implementations, the WME can include a liquid-crystalphase-only spatial light modulator. In another implementation, the WMEcan include a ferroelectric binary spatial light modulator. In otherimplementations, the WME 1912 can include a deformable mirror (e.g., apiston-tip-tilt mirror) or an array of micromirrors. By controlling theWME 1912 (e.g., by control of the individual pixels of a spatial lightmodulator or individual mirrors within an array of micrometers orcontrol of individual elements of a piston-tip-tilt mirror), thewavefront of the light reflected from the WME 1912, and consequently thewavefront(s) of downstream beam(s) (e.g., beams in the sample 1946), canbe controlled. For example, the WME 1912 can be programmed to modulatethe wavefront of the incoming light beam such that the outgoing lightbeam from the WME subsequently defines an array of coherent Bessel-likebeams that overlap and interfere with each other to create a plane ofstructured illumination in the sample 1946. The WME 1912 can beoptically conjugated to the sample 1946, so that modulations introducedby the WME can be propagated to the sample.

The WME 192 can be used to control the relative phases of individualbeamlets (or portions of the incoming wavefront) that are reflected fromthe WME. For example, the WME 1912 can be used to control the relativephases of individual portions of the wavefront that strike the WME 1912and that then propagate into the sample 1946. In some implementations,this relative phase control of individual portions of the reflected wavefront can result in control of relative phases of individual Bessel-likebeams in array of beams in the sample 1946.

In some implementations, the WME 1912 can include a spatial lightmodulator, and in some implementations the spatial light modulator canbe a binary spatial light modulator, in which each pixel of the spatiallight modulator can have one of two different states that affect thelight modulated by the pixel. In some implementations, the WME 1912 canbe used to scan the array of Bessel-like beams within the sample—eitherwithin the plane of the array or perpendicular to the plane (e.g. in theZ axis direction).

An advantage of using a reflective spatial light modulator (SLM) as theWME is that, with a high number of pixels (e.g., 1024×1280 pixels), itcan be readily divided into many subregions, and in part because thesubregions are truly independent, and not mechanically coupled, as in adeformable mirror.

After modulation by the WME 1912, the light reflected from the WME canbe reflected by the beam splitter 1908 and reflected by mirrors 1914,1916. Then, the light can be imaged by a lens 1918 onto an apodizationmask 1920 that is conjugate to the rear pupil of the excitationobjective 1942. After the apodization mask 1920, the light can bereflected off of a mirror 1922, transmitted through relay lenses 1924,1926, reflected off galvanometer mirror 1928, mirror 1930, transmittedthrough relay lenses 1932, 1934, reflected off galvanometer mirror 1936,and transmitted through relay lenses 1938, 1940 to the rear pupil planeof excitation objective 1942. Then, the light can be focused byexcitation objective 1942 onto the sample 1946 that is housed in chamber1944.

Mirror 1928 can operate as a galvanometer-type mirror to translate thestructured plane illumination in the X direction within the sample, andthe mirror 1928 can be conjugated to the apodization mask 1920 by relaylenses 1924, 1926. Mirror 1936 can operate as a galvanometer-type mirrorto translate the structured plane illumination in the Z direction withinthe sample, and the mirror 1936 can be conjugated to mirror 1928 byrelay lenses 1932, 1934. The rear pupil plane of excitation objective1942 can be conjugated to mirror 1936 by relay lenses 1938 and 1940. Thecombination of lenses 1918, 1924, 1926, 1932, 1934, 1938, and 1940 aswell as excitation objective 1942 then serve to conjugate WME 1912 to anexcitation plane within the sample 1946. The sample 1946 can besupported on a translation stage 1947 that can be used to translate thesample in space. In some implementations, the translation stage 1947 cantranslate the sample 1946 with respect to a beam of radiation that isprovided to the sample, while the position of the beam remains fixed.

Light emitted from the sample 1946 due to the interaction of theexcitation light with the sample can be collected by the detectionobjective 1948 and then focused by lens 1950 onto a detector 1952.Information collected by the detector 1952 can be sent to a computingdevice 1954, which may include one or more processors and one or morememories. The computing device may process the information from thedetector 1952 to create images of the sample 1946 based on theinformation provided by the detector 1952.

The WME 1912 can control the wavefront of the light leaving the WME,such that the plurality of Bessel-like beams is created in the sample1946. Furthermore, the WME 1912 can control the relative phases of theindividual Bessel-like beams in the sample. The relative phases of theindividual Bessel-like beams can be controlled such that neighboringBessel-like beams interfere destructively with each other at positionsthat are out of the plane of the array of Bessel-like beams. Forexample, the destructive interference can occur within the Z≠0 planewhen the array of Bessel-like beams is in the Z=0 plane. For example,the first side lobes of neighboring Bessel-like beams can destructivelyinterfere where they intersect with each other at locations that are notin the plane of the array. For example, the intersection point can occurat a position that is closer to the plane of the array than a diameterof the first side lobe of the Bessel-like beams. Techniques for using aspatial light modulator WME to create structured light sheets within thesample are described in more detail below.

FIG. 20 is a flowchart of a process 2000 of determining a pattern toapply to a binary spatial light modulator, which will produce a coherentstructured light sheet having a relatively low thickness in the Zdirection over a sufficient length in the Y direction to image samplesof interest. In the process 2000, the complex electric fieldE _(b)(x,z)of a single Bessel-like beam propagating in the Y direction into thesample is calculated (step 2002). The complex electric field is chosenbased on a maximum NA to achieve a desired maximum X-Z spatial frequencyand based on a minimum NA to achieve a desired beam length in the Ydirection. Then, the complex electric fieldE _(tot)(x,z)of the structured light sheet that is formed by a coherent sum of aplurality of Bessel-like beams in a linear periodic array of Bessel-likebeams can be calculated (step 2004). The total complex electric field ofthe array of beams can be expressed as:

${E_{tot}\left( {x,z} \right)} = {\sum\limits_{n = 1}^{N}\;{{\exp\left( {{in}\;\alpha} \right)}{E_{b}\left( {{x + {nT}},z} \right)}}}$where α is the phase difference between adjacent beams in the array, andfor T is the spatial period of the array of beams. In someimplementations, α can be set equal to 0 or π (i.e., all beams can havethe same phase, or beams can have alternating opposite phases). Then,the real scalar field in the desired polarization state can bedetermined (step 2006), where the real scalar field is given by:E _(tot)(x,z)=Re{E _(tot)(x,z)·e _(d)}.

Next, the real scalar field can be multiplied by an envelope functionψ(z) that bounds the excitation light to the desired vicinity of theideal Z=0 illumination plane (step 2008). The product of the real scalarfield and the envelope function gives the function for the bound field:E _(bound)(x,z)=ψ(z)E _(tot)(x,z).In some implementations, the envelope function can be a Gaussianfunction:ψ(z)=exp(−z ² /a ²)Then, the field values having a magnitude lower than a threshold value,ϵ, can be set to zero (step 2010). The thresholding step can beexpressed mathematically as:E _(thresh)(x,z)=Θ(|E _(bound)(x,z)|−ϵ)E _(bound)(x,z)where Θ(ξ)=1, for ξ>0 and 0 for ξ<0. Then, individual pixels values of abinary SLM that is used as the WME 1912 can be set to impose a 0 or πphase shift on light that interacts with the SLM (step 2012), accordingto:SLM(x _(p) ,z _(p))=Θ(E _(thresh)(x _(p) ,z _(p)))π,where the “p” subscript references an individual pixel of the SLM.

FIG. 21 shows a series of graphical illustrations of the process 2000,when the processes used to generate a thin array of structuredexcitation radiation is swept in the X direction to generate a plane ofexcitation illumination. FIG. 21A illustrates a cross-sectional profilein the X-Z plane of a Bessel like beam propagating in the Y direction.The particular cross section shown in FIG. 21A is for a Bessel-like beamhaving a maximum numerical aperture of 0.60 and a minimum numericalaperture of 0.54. Higher electric field strengths are shown by whiterregions in FIG. 21A.

FIG. 21B illustrates the electric field, in the X-Z plane, of astructured light sheet formed by coherent sum of a linear, periodicarray of Bessel-like beams that propagate in the Y direction. Theindividual Bessel-like beams have a maximum numerical aperture of 0.60and a minimum numerical aperture is 0.54. The wavelength of the light is488 nm, and the period of the array of beams is 0.90 μm, and theindividual beams of the array all have the same phase. Higher electricfield strengths are shown by whiter regions in FIG. 21B. The lengthsshown on the axes of all of the panels of FIG. 21 are normalized thewavelength of light in the medium within the sample chamber 1944.

FIG. 21C illustrates the electric field, in the XZ plane, of thestructured light sheet of FIG. 21B after a Gaussian envelope functionhas been applied to the field of the light sheet to bound the lightsheet in the Z direction. Higher electric field strengths are shown bywhiter regions. FIG. 21D illustrates the pattern of phase shifts appliedto individual pixels of a binary spatial light modulator to generate thefield shown in FIG. 21C. Pixels generating a phase shift of π are shownin black, and pixels generating a phase shift of zero are shown inwhite. FIG. 21E illustrates the cross-sectional point spread function,in the X-Z plane, of the structured plane of excitation radiation thatis produced in the sample by the coherent array of Bessel-like beams,which are generated by the pattern on the spatial light modulator shownin FIG. 21D. Higher light intensities are shown by whiter regions. FIG.21F illustrates the excitation beam intensity that is produced in thesample when the array of Bessel-like beams is swept or dithered in the Xdirection. Higher intensities are shown by whiter regions.

Changing the period of the array of the coherent Bessel-like beams canaffect the overall electric field pattern resulting from theinterference of the plurality of beams. In particular, for differentperiods of the array, the resulting electric field interference patterncan extend relatively more or less in the Z direction. This effect canbe exploited to determine parameters of the coherent array that can beuseful for generating images of the sample using super resolutionstructured illumination techniques as well as using a thin sheet ofstructured illumination that is swept in the X direction.

FIG. 22 shows a series graphical illustrations of the process 2000, whenthe plane is used to generate an array of structured excitationradiation that is used to generate images of the sample using superresolution structured illumination techniques. Like FIG. 21A, FIG. 22Aillustrates a cross-sectional profile in the X-Z plane of a Bessel likebeam propagating in the Y direction. The particular cross section shownin FIG. 22A is identical to that of FIG. 21A and is for a Bessel-likebeam having a maximum numerical aperture of 0.60 and a minimum numericalaperture of 0.54. The lengths shown on the axes of all of the panels ofFIG. 22 are normalized the wavelength of light in the medium within thesample chamber 1944.

FIG. 22B illustrates the electric field, in the X-Z plane, of astructured light sheet formed by a coherent sum of a linear, periodicarray of Bessel-like beams that propagate in the Y direction. Theindividual Bessel-like beams have a maximum numerical aperture of 0.60and a minimum numerical aperture is 0.54. The wavelength of the light is488 nm, and the period of the array of beams is 0.92 μm and theindividual beams of the array all have the same phase. Thus, the periodof the array illustrated in FIG. 22B is 0.02 μm longer than the periodof the array illustrated in FIG. 21B.

FIG. 22C illustrates the electric field, in the XZ plane, of thestructured light sheet of FIG. 22B after a Gaussian envelope functionhas been applied to the field of the light sheet to bound the lightsheet in the Z direction. Because the structured light sheets shown inFIG. 22 are to be used for super resolution structured illuminationmicroscopy, in which it may be desirable to have the electric fieldextend further in the Z direction then when using the light sheet in aswept sheet mode, and therefore the envelope (or “bounding”) functionused in FIG. 22C may be relatively more relaxed than the boundingfunction used in FIG. 21C.

FIG. 22D illustrates the pattern of phase shifts applied to individualpixels of a binary spatial light modulator to generate the field shownin FIG. 22C. Pixels generating a phase shift of π are shown in black,and pixels generating a phase shift of zero are shown in white. FIG. 22Eillustrates the cross-sectional point spread function, in the X-Z plane,of the structured plane of excitation radiation that is produced in thesample by the coherent array of Bessel-like beams, which are generatedby the pattern on the spatial light modulator shown in FIG. 22D. FIG.22F illustrates the modulation transfer function, which corresponds tothe point spread functions shown in FIG. 22E. All of the MTFs arenormalized to 4π/λ, where λ is the wavelength of light in the mediumwithin the sample chamber 1944.

As can be seen from the electric field patterns and point spreadfunction patterns in FIGS. 21 and 22, the coherent superposition of aplurality of Bessel-like beams bears little resemblance to the electricfield patterns and point spread function patterns of individualBessel-like beams. As is evident from a comparison of FIG. 21 and FIG.22, changing the period of the array of beams causes large changes inoptical properties of the optical lattices (e.g., the period, symmetry,and degree of bounding in the Z direction of the lattices) that resultfrom interference between the beams of the array. Instead, the coherentsuperposition of an array of Bessel-like beams, in general, forms aspatially-structured plane of excitation radiation that can be used toexcite optical labels within a sample, which then emit light that isdetected and used to generate an image of the sample. In someimplementations, the spatially-structured plane of excitation radiationcan be swept in a direction parallel to the plane to generate a thinsheet of excitation radiation. In some implementations, thespatially-structured plane of excitation radiation can be translated indiscrete steps in a direction parallel to the plane and emit light canbe detected when the plane is in each of the different positions. Then,the light detected from the sample when the plane is in each of thedifferent positions can be algorithmically combined to generate a superresolution image of the sample.

FIG. 23 is a schematic diagram of the intensities of different modes ofexcitation radiation that is provided to the sample. FIG. 23A is across-sectional in the X-Z plane of a Bessel-like beam propagating inthe Y direction. The particular cross section shown in FIG. 23A is for aBessel-like beam having a wavelength of 488 nm and having a maximumnumerical aperture of 0.60 and a minimum numerical aperture of 0.54.Higher intensities are shown by whiter regions. When the Bessel-likebeam of FIG. 23A is swept in the X direction, then the time-averagedintensities in the X-Z plane shown in FIG. 23B results. FIG. 23C is across-sectional in the X-Z plane of a superposition of incoherentBessel-like beams propagating in the Y direction, such as would occur ifthe single Bessel-like beam in FIG. 23A were moved in discrete steps.The pattern shown in FIG. 23C is for a 488 nm Bessel-like beam having amaximum numerical aperture of 0.60 and a minimum numerical aperture of0.54, stepped in units of 0.90 μm. When multiple instances of the arrayof Bessel-like beams of FIG. 23C are moved in small increments in the Xdirection and the resulting signal integrate don a camera, then thetime-averaged intensity in the X-Z plane shown in FIG. 23D results. FIG.23E is a cross-section in the X-Z plane of a superposition of coherentBessel-like beams propagating in the Y direction. The pattern shown inFIG. 23E is for an array of 488 nm Bessel-like beams having a maximumnumerical aperture of 0.60 and a minimum numerical aperture of 0.54,with individual beams of the array being spaced 0.90 μm from each other.When the array of Bessel-like beams of FIG. 23E is swept or dithered inthe X direction, then the time-averaged intensity in the X-Z plane shownin FIG. 23F results. As can be seen by a comparison of FIG. 23B, FIG.23D, and FIG. 23F, the coherent array of Bessel-like beams can result ina light sheet that is more tightly confined in the Z direction that alight sheet that is produced by sweeping a single Bessel-like beams(FIG. 23B) or a light sheet that is produced by sweeping an incoherentarray of Bessel-like beams (FIG. 23D).

Referring again to the electric field patterns in FIGS. 21B and 22B, andpoint spread function intensity patterns in FIGS. 21E and 22E, it can beseen that the coherent superposition of a plurality of Bessel-like beamsforms a spatially-structured plane of excitation radiation. Thesepatterns can be viewed as optical lattices that are created byinterference within the sample between different beamlets of the beamthat is modulated by the spatial light modulator 1912 shown in FIG. 19and then enter the sample 1946 through the excitation objective 1942.Therefore, in some implementations, a pattern can be applied to the WME1912 that creates an optical lattice within the sample, which can beused to generate a spatially-structured plane of excitation radiationthat can be used to generate images of the sample 1946.

FIG. 24 is a flowchart of a process 2400 of determining a pattern toapply to a binary spatial light modulator, which will produce an opticallattice within the sample, where the optical lattice can be used as acoherent structured light sheet having a relatively low thickness extentin the Z direction over a sufficient length in the Y direction to imagesamples of interest. In the process 2400, the complex electric fieldE_(lattice)(x,z) of a selected two-dimensional 2D optical lattice can becalculated (step 2402). The selected optical lattice can be, forexample, a fundamental lattice, a sparse lattice, a composite lattice,or a maximally symmetric composite lattice, as described in U.S. Pat.No. 7,609,391, entitled “Optical Lattice Microscopy,” issued on Oct. 27,2009, which is incorporated herein by reference. In someimplementations, a maximally symmetric composite lattice can be selectedto provide tight confinement of the excitation radiation in the Zdirection when generating images of the sample using the swept sheetmode and to provide high spatial frequency components in the XZ planewhen generating images of the sample using the super resolution,structured illumination mode. In some implementations, maximallysymmetric composite hexagonal and square lattices can be used, becausethey can provide more wavevectors than lattices with other symmetry.

Then, the lattice can be rotated about the Y axis to a desiredorientation (step 2404). For example, an orientation of the lattice inwhich lattice wavevectors lie along the X axis facilitates theconstruction of structured light sheets that are tightly confined in theZ direction. In another example, an orientation of the optical latticein which a line of lattice intensity maxima lies along the x-axis can bedesirable. In another example, an optical lattice having a periodicityand orientation such that adjacent lines of the lattice maximum alongthe X direction are separated by more than the desired light sheetthickness in the Z direction can be useful when using the lattice togenerate images of the sample with the swept sheet mode. However, thelines of lattice maximum along the X direction should be separated byless than the desired light sheet thickness when using the superresolution, structured illumination mode to generate images of thesample.

After the orientation of the lattice is determined, the real scalarfield of the optical lattice can be determined (step 2406), where thereal scalar field is given by:E _(lattice)(x,z)=Re{E _(lattice)(x,z)·e _(d)},Where e_(d) is a vector in the direction of the desired polarization ofthe electric field. Next, the real scalar field of the optical latticecan be multiplied by an envelope function ψ(z) that bounds theexcitation light to the desired vicinity of the ideal Z=0 illuminationplane (step 2408). The product of the real scalar field and the envelopefunction gives the function for the bound field:E _(bound)(x,z)=ψ(z)E _(lattice)(x,z).In some implementations, the envelope function can be a Gaussianfunction:ψ(z)=exp(−z ² /a ²)Then, the field values having a magnitude lower than a threshold value,ϵ, can be set to zero (step 2410). The thresholding step can beexpressed mathematically as:E _(thresh)(x,z)=Θ(|E _(bound)(x,z)|−ϵ)E _(bound)(x,z)where Θ(ξ)=1, for ξ>0 and 0 for ξ<0. Then, individual pixels values of abinary SLM that is used as the WME 1912 can be set to impose a 0 or πphase shift on light that interacts with the SLM (step 2412), accordingto:SLM(x _(p) ,z _(p))=Θ(E _(thresh)(x _(p) ,z _(p)))π,where the “p” subscript references an individual pixel of the SLM. Thispattern imposed on the SLM, which is conjugate to the sample 1946, willcreate an optical lattice within the sample.

FIG. 25 shows a series of graphical illustrations of the process 2400,when the process is used to generate an optical lattice of structuredexcitation radiation that is swept in the X direction to generate aplane of excitation illumination. FIG. 25A illustrates a cross-sectionalprofile in the X-Z plane of an ideal two-dimensional fundamentalhexagonal lattice that is oriented in the Z direction. The opticallattice is formed by the coherent superposition of a plurality of beamsthat all converge on a cone corresponding to a numerical aperture of0.51. The profile shows the real electric field strengths in the opticallattice, with higher electric field strengths being shown by whiterregions. The lengths shown on the axes of all of the panels of FIG. 25are normalized the wavelength of light in the medium within the samplechamber 1944.

FIG. 25B illustrates the electric field, in the XZ plane, of the opticallattice of FIG. 25A after a Gaussian envelope function has been appliedto the optical lattice to bound the lattice in the Z direction. Higherelectric field strengths are shown by whiter regions. FIG. 25Cillustrates the pattern of phase shifts applied to individual pixels ofa binary spatial light modulator to generate the field shown in FIG.25B. Pixels generating a phase shift of π are shown in black, and pixelsgenerating a phase shift of zero are shown in white. FIG. 25Dillustrates the cross-sectional point spread function, in the X-Z plane,of the structured plane of excitation radiation that is produced in thesample by the optical lattice, which is generated by the pattern on thespatial light modulator shown in FIG. 25C, and then filtered by anannular apodization mask that limits the maximum NA of the excitation to0.55 and the minimum NA of the excitation to 0.44. Higher intensitiesare shown by whiter regions. FIG. 25E illustrates the excitation beamintensity that is produced in the sample when the bound optical latticepattern in FIG. 25D is swept or dithered in the X direction. Higherintensities are shown by whiter regions.

FIG. 26 illustrates the light patterns at a plurality of locations alongthe beam path shown in FIG. 19 when the pattern shown in FIG. 25C isused on the SLM 1912. For example, FIG. 26A is identical to FIG. 25C andillustrates the pattern of phase shifts applied to individual pixels ofa binary spatial light modulator 1912 to generate the field shown inFIG. 25B. FIG. 26B illustrates the intensity of light that impinges onthe apodization mask 1920 downstream from the SLM 1912. FIG. 26Cillustrates the transmission function of the apodization mask 1920, andFIG. 26D illustrates the intensity of light immediately after theapodization mask 1920. As shown in FIG. 26D, the pattern of the lightthat exists just after the apodization mask 1920, which is conjugate tothe rear pupil of the excitation objective, is a plurality of sixvertical slits located on a surface of a cone, and when this pattern isfocused by the excitation objective 1942 to the focal plane within thesample, the optical lattice shown in FIG. 26E (which is identical to thepattern shown in FIG. 25D) results. When this optical lattice is sweptor dithered in the X direction, the sheet of excitation radiation shownin FIG. 26F results. The lengths shown on the axes of all of the panelsof FIG. 26 are normalized the wavelength of light in the medium withinthe sample chamber 1944.

FIG. 27 shows a series of graphical illustrations of the process 2400,when the processes used to generate an optical lattice of structuredexcitation radiation that is translated in the X direction in discretesteps to generate images of the sample using superresolution, structuredillumination techniques. FIG. 27A illustrates a cross-sectional profilein the X-Z plane of a two-dimensional fundamental hexagonal lattice thatis oriented in the Z direction. The optical lattice is formed by thecoherent superposition of a plurality of beams that all converge on acone corresponding to a numerical aperture of 0.57. The lengths shown onthe axes of all of the panels of FIG. 27 are normalized the wavelengthof light in the medium within the sample chamber 1944.

FIG. 27B illustrates the electric field, in the XZ plane, of the opticallattice of FIG. 27A after a Gaussian envelope function has been appliedto the optical lattice to bound the lattice in the Z direction. Higherelectric field strengths are shown by whiter regions. The envelopefunction used for FIG. 27B confines the lattice less tightly in the Zdirection that the envelope function used for FIG. 25B. FIG. 27Cillustrates the pattern of phase shifts applied to individual pixels ofa binary spatial light modulator to generate the field shown in FIG.27B. Pixels generating a phase shift of π are shown in black, and pixelsgenerating a phase shift of zero are shown in white. FIG. 27Dillustrates the cross-sectional point spread function, in the X-Z plane,of the structured plane of excitation radiation that is produced in thesample by the optical lattice, which is generated by the pattern on thespatial light modulator shown in FIG. 27C, and then filtered by anannular apodization mask that limits the maximum NA of the excitation to0.60 and the minimum NA of the excitation to 0.54. Higher intensitiesare shown by whiter regions. FIG. 27E illustrates the modulationtransfer function, in reciprocal space, which corresponds to theintensity pattern shown FIG. 27D. The MTF is normalized to 4π/λ, where λis the wavelength of the excitation radiation. Higher spectral powersare shown by whiter regions.

FIG. 28 illustrates the light patterns at a plurality of locations alongthe beam path shown in FIG. 19 when the pattern shown in FIG. 27C isused on the SLM 1912. For example, FIG. 28A is identical to FIG. 27C andillustrates the pattern of phase shifts applied to individual pixels ofa binary spatial light modulator 1912 to generate the field shown inFIG. 27B. FIG. 28B illustrates the intensity of light that impinges onthe apodization mask 1920 downstream from the SLM 1912 when the SLMincludes the pattern of FIG. 28A. FIG. 28C illustrates the transmissionfunction of the apodization mask 1920, and FIG. 28D illustrates theintensity of light immediately after the apodization mask 1920. The maskused to produce the transmission function shown in FIG. 28C includes theproduct of an annular mask and a mask having two slits, which transmitsonly three of the six beams shown in FIG. 28B. As shown in FIG. 28D, thepattern of the light that exists just after the apodization mask 1920,which is conjugate to the rear pupil of the excitation objective, is aplurality of three vertical slits located on a surface of a cone, andwhen this pattern is focused by the excitation objective 1942 to thefocal plane within the sample, the optical lattice shown in FIG. 28E(which is identical to the pattern shown in FIG. 27D) results. Themodulation transfer function for this lattice is shown in FIG. 28F. Thelengths shown on the axes of all of the panels of FIG. 28 are normalizedthe wavelength of light in the medium within the sample chamber 1944.

Referring again to FIG. 25, and, in particular, to FIG. 25B, theenvelope function that are selected to bound the optical lattice to thevicinity of the Z=0 plane of the sample can have an effect on theintensity pattern of the swept light sheet shown in FIG. 25E. Forexample, when a strong envelope function is selected that tightly bindsthe optical lattice to the vicinity of the Z=0 plane, then the intensityof the optical lattice may be strongly confined to the line of intensitymaxima along the Z=0 plane, but the extent of the individual maxima inthe Z direction can be relatively large. On the other hand, when a weakenvelope function is selected that only loosely binds the opticallattice to the vicinity of the Z=0 plane, then the optical latticewithin the sample may include intensity maxima along the line of the Z=0plane and also maxima along one or more lines that are displaced fromthe Z=0 plane. This phenomenon is shown in FIG. 29.

FIG. 29 is a plurality of graphs illustrating the effect of the Z axisbounding of the optical lattice on the light sheets produced in thesample. FIG. 29A illustrates the intensity of the optical lattice towhich a wide, or weak, envelope function is applied. As can be seen inFIG. 29A, intensity maxima exist along the Z=0 plane and also a positiveand negative nonzero values of Z. Sweeping or dithering this pattern inthe X direction creates a light sheet whose intensity profile along theZ direction is shown in the curve A of FIG. 29B. Curve A shows sidelobes peaked at three wavelengths away from the Z=0 plane. Curve B shownin FIG. 29B shows the point spread function of the detection objective1948, and the curve C in FIG. 29B shows the normalized product of curvesA and B, which is the overall point spread function of the opticalsystem in the Z direction. In some implementations, the numericalaperture of the excitation objective and the numerical aperture of thedetection objective can be selected such that the maximum intensity of aside lobe of the sheet of excitation illumination occurs at a Z positionthat corresponds to a minimum in the point spread function of thedetection objective. In this manner, the overall point spread functionshown in curve C can minimize the effect of the excitation illuminationside lobes on images generated from the sample. The lengths shown on theaxes of all of the panels of FIG. 29 are normalized the wavelength oflight in the medium within the sample chamber 1944.

FIG. 29G illustrates the intensity of the optical lattice to which anarrow, or strong, envelope function is applied to the ideal opticallattice pattern. As can be seen in FIG. 29G, intensity maxima existalong the Z=0 plane, but there are no lines of intensity maxima alongother planes. Sweeping or dithering this pattern in the X directioncreates a light sheet whose intensity profile along the Z direction isshown in curve A of FIG. 29H. Curve A shows much smaller side lobespeaked at three wavelength away from the Z=0 plane than in FIG. 29B.Curve B shown in FIG. 29H shows the point spread function of thedetection objective 1948, and curve C in FIG. 29H shows the normalizedproduct of curves A and B, which is the overall point spread function ofthe optical system in the Z direction. As can be seen from a comparisonof FIG. 29B and FIG. 29H, the central peak in curve A of FIG. 29B isnarrower than the central peak in curve A of FIG. 29H, but the sidelobes of FIG. 29B are larger than the side lobes and FIG. 29H. Thus,bound optical lattices having different parameters can be selected toimage different samples using different techniques. FIG. 29C and FIG.29D are similar to FIGS. 29A and 29B, respectively, and to FIGS. 29G and29H, respectively, except that a medium-wide envelope function is used.FIG. 29E and FIG. 29F are similar to FIGS. 29A and 29B, respectively,and to FIGS. 29G and 29H, respectively, except that a medium-narrowenvelope function is used.

Stochastic Excitation and Bessel-Like Beams

Another technique that can be used to create high-resolution images of asample involves using stochastic activation and/or excitation ofindividual emitting labels within a sample (for example, such asdescribed in U.S. Pat. No. 7,782,457, which is incorporated herein byreference) along with activation radiation and/or excitation radiationthat is provided to the sample in the form of a thin sheet of radiation.In this manner, individual emitters within the sample can beindividually resolved as their emission of signal light is turned on andoff, and the thin sheet of activation and/or excitation radiation canlimit the amount of signal light that is produced in portions of thesample that are not in the focal plane of the detection objective.During the stochastic activation of labels, as different emitting labelsare turned on and off within a focal plane of the detection objective,an image of the sample at that plane can be built up over time. Also,the focal plane of the detection objective can be moved through thesample, and the thin sheet of activation and/or excitation radiation canbe moved along with the focal plane, so that multiple planes of thesample can be imaged, which may allow generation of a three-dimensionalimage of the sample.

In some implementations, a sample can include a dense plurality ofphototransformable or photoswitched optical labels (“PTOLs”), such as,for example, photoactivated or photoswitched fluorescent proteins(“FPs”), that are transformable from an inactive state (in which thelabels do not produce significant detectable radiation when excited) toan activated state (in which the labels can emit radiation when excited)by virtue of the interaction of the transformable labels with theirenvironment. With sufficient control over at least one activatingenvironmental parameter, a controllable, sparse subset of the labels canbe activated. These activated labels can then be excited into excitedstates, from which they can emit fluorescence radiation that can beimaged by an optical system. By controlling the activation environmentand exciting radiation, the mean volume per activated and excited labelthat emits radiation can be greater than the diffraction-limitedresolution volume (“DLRV”) characteristic of the optical system. Bydetecting radiation from such a sparse subset of emitting labels, thelocation of the activated and excited PTOLs can be determined withsuperresolution accuracy. Then, the activated labels can be deactivated,and another subset of transformable labels, statistically likely to belocated at different positions within the sample, can be activated bycontrolling at least one activating environmental parameter, andfluorescence from the second subset of activated labels can be imaged,and their locations can be determined with superresolution accuracy.This process can be repeated to determine the location of moretransformable labels within the sample with superresolution accuracy.The determined locations of all the transformable labels from thedifferent images can be combined to build up a superresolution image ofthe sample.

FIG. 30 is a schematic diagram illustrating a PTOLs (e.g., a fluorescentmolecule) 3001 stimulated by excitation radiation 3002 from a groundstate into an excited state 3003 that emits a portion of the energy ofthe excited state into a fluorescence radiation photon 3004. Themolecule 3001 then reverts to the ground state 3005. This cycle ofexcitation of the molecule 3001 by radiation 3002 and emission offluorescence radiation 3004 can be repeated many times 3006, and thefluorescence radiation can be accumulated by a microscope camera ordetector. If there are many such fluorescent molecules 3001 within adiffraction limited resolution volume (“DLRV”) of the imaging optics itmight seem difficult to distinguish the fluorescence radiation of onemolecule from another molecule.

However, in the case of a phototransformable optical label (“PTOL”)molecule or emitter 3011, the ability of the PTOL to absorb excitationradiation and therefore to emit fluorescence radiation can be explicitlyturned on by an activating signal, and in certain cases, can be turnedoff by a de-activating signal. In an inactivated state, a PTOL 3011 canbe exposed to excitation radiation 3012 having a characteristicwavelength, but it will radiate little, if any, fluorescence radiationat a wavelength characteristic of an activated and excited PTOL.However, when the PTOL 3021 is irradiated with activation radiation3022, the PTOL 3021 can be transformed into an excitable state 3023. Theactivation radiation 3022 often has a different wavelength than thewavelength of the excitation radiation, but for some PTOLs activationradiation and excitation radiation have the same wavelength and aredistinguished by their intensities. After a PTOL is transformed into anexcitable state 3023, subsequent illumination of the activated PTOL 3023by excitation radiation 3024 generally results in detectable emission offluorescence radiation 3026. This process of excitation and emission canbe repeated numerous times 3028 for an activated PTOL 3027 until thePTOL eventually bleaches or deactivates, at which point the PTOL 3029can no longer be excited and can no longer emit fluorescence radiation.

Thus, a PTOL 3021 can be illuminated with activation radiation 3022 totransform the PTOL into an activated state 3023. The activated PTOL 3023can be illuminated with excitation radiation 3024 to excite the PTOLinto an excited state 3025, from which the PTOL 3025 can emit radiation3026. For some species of PTOL, the PTOL can be transformed from anactivated state 3023 back to an unactivated state 3021, either throughspontaneous decay to the unactivated state or through the application ofde-activation radiation.

A fluorescent protein (“FP”) is a particular kind of phototransformableoptical label (“PTOL”) whose optical properties can be altered by lightand that can be used to label a portion of a sample to image opticallythe portion of the sample. As used herein “fluorescence” and“fluorescent” generally designate an optical response of the PTOL. Inaddition to the common understanding of fluorescence (e.g., emission ofa photon from a substance in response to excitation by a more energeticphoton) we include other properties that can characterize the PTOL. Forexample, we include emission of a photon in response to multi-photonexcitation, or a large elastic optical cross section that can beactivated or deactivated.

PTOLs useful for superresolution via localization of isolated PTOLsgenerally have one or more of the following distinguishingcharacteristics: a relatively high brightness (as defined by itsexcitation cross section and the quantum efficiency); a relatively highcontrast ratio between luminescence generated in the activated state tothat generated in the inactivated state (which might be improved througha judicious choice of the excitation wavelength and detection filterset); an excitation wavelength that reduces autofluorescence from othercellular material exposed to the excitation; an emission wavelength thatis sufficiently different from the spectral range over which mostautofluorescence occurs; and photostability that is large enough that asufficient number of photons are collected from each PTOL to achieve thedesired localization accuracy prior to irreversible bleaching, yet, forPTOLs other than the kindling proteins and Dronpa that can switch backto the deactivated state, is nevertheless still finite, so that a newpopulation of individually resolvable activated PTOLs can be createdafter the current set is largely bleached. Indeed, to reduce possiblephototoxicity related to irreversible photobleaching, an ideal PTOLwould remain in the activated state until it is deactivated by choiceusing other means (e.g., illumination at a separate deactivationwavelength).

Photoactivatable fluorescent proteins useful for superresolutionmicroscopy include, for example, Aequorea victoria photoactivated greenfluorescent protein (“PA-GFP”), Photoswitchable cyan fluorescent protein(“PS-CFP”), Kaede, Kindling fluorescent proteins (“KFP”), and Dronpa.Superresolution via localization has been demonstrated with thetetrameric PTOLs Kaede and Kikume, as well as the monomeric, dimeric,and tandem dimer forms of EosFP. These PTOLS have the common advantagesof large wavelength spread between the inactivated and activatedabsorption and emission maxima, high brightness, and longer wavelengthemission, where autofluorescence is typically lower. Monomeric EosFP hasthe added advantage of smaller physical size than tetrameric Kaede orKikume, and may therefore be less perturbative of cellular structure andfunction. In practice, a particular FP could be selected from a numberof different FPs based on a user's criteria for optimization for a givenapplication. Given the diversity of PTOL species with differentactivation, excitation, and emission wavelengths and time constants, itis possible to construct separate images for each species of PTOLs.Thus, different components of a sample can be tagged with distinctlabels, and each labeled object can then be independently identified ina super-resolution image that can be constructed as disclosed herein.

It is possible to label specific sample features of interest with PTOLs,such that the PTOLs, and therefore the specific sample features, can beimaged. For PTOLs that can be genetically expressed (e.g., thephotoactivable fluorescent proteins), DNA plasmids can be created andinserted into the cell by transient transfection, so that fluorescentprotein PTOLs are produced fused to specific proteins of interest.Likewise, stable transfections that permanently alter the genetic makeupof a cell line can be created, so that such cells produce fluorescentprotein PTOLs. PTOLs also can be tagged to specific cellular featuresusing immumolabeling techniques, or high-specificity small moleculereceptor-ligand binding systems, such as biotin ligase.

Radiation from molecules or emitters can be used for sub-diffractivelocalization of PTOLs when the radiating molecules or emitters areisolated and spaced further apart from each other than the diffractionlimited length scale of the imaging optics. For example, as shown inFIG. 31, excitation radiation 3101 can excite an isolated emitter 3102into an excited state 3103. Outgoing radiation 3104 emitted from theexcited emitter 3103 can be collected by microscope optics including adetection objective 3105 and refocused 3106 onto a diffraction limitedspot 3107. This spot profile is shown plotted on the axis of position3108 versus emission intensity 3109 in the image plane 3108. The imageand object plane are scaled by the magnification M. In the image plane3108, the minimum spatial width of this spot is characterized by afundamental limitation of resolution of microscopes and is given by theAbbe criteria Δ≈0.5*λ*M/NA, where λ is the wavelength of emissionradiation 3104 and NA is the numerical aperture of the objective 3105.This magnified image of the isolated emitter can be used to localize theemitter to sub-diffractive precision by measuring the distribution ofthe emission at a detector such as a CCD camera. This data can then befit or otherwise processed to find the center of the detected signal.For example, the emission intensity profile of light emitted from a PTOLand detected on a detector can be characterized by the discrete dataset, {n_(i)}, where n_(i) are the number of photons detected in thei^(th) pixel of the detector located at position x_(i). This data can befit to a peaked function to determine a location of the PTOL. Forexample, a Gaussian function,

${n_{i} = {\frac{N}{\sqrt{2\pi}\sigma}{\mathbb{e}}^{- \frac{{({x_{i} - x_{c}})}^{2}}{2\sigma^{2}}}}},$

can be used to perform the fit. A least squares fit of the data to thepeaked function, for example, can find a value for the peak centerlocation x_(c). In addition other parameters, such as, for example, thetotal number of photons detected, N, and the peak width, σ, (which canbe generally on the order of Δx) can also be deduced from the fit.Errors in n_(i) can be expressed by a value, δn_(i), and likewise theuncertainty in the center position, x_(c), can be expressed as through aparameter, δx. In particular, when the system noise is limited by photonshot noise statistics (meaning δn_(i)=sqrt(n_(i))) arising from thedetected signal and N is the number of photons detected, then theaccuracy to which this center can be localized is given byδx=Δx/sqrt(N). To the extent that N is much larger than unity, thelocalization accuracy 3110 can be significantly better than thediffraction limit 3121. The data also can be fit to other functions thanthe Gaussian function to determine a center location and width of theposition of a PTOL.

However, it can be difficult to apply this technique to a set ofcontinuously-emitting fluorescent molecules 3112 that are spaced soclosely together that they are within Δx of each other. In this case,the diffractive spots are highly overlapped, such that fitting of theimage of a molecule to obtain a position of the molecule withsuperresolution accuracy is difficult. Thus, in this situation theresolution limit generally is given by standard Abbe criterion 3121,i.e. the width of the diffractive limited spot.

However, by selectively activating and de-activating subsets of PTOLswithin a dense set of PTOLs this localization concept can be used evenwhen the optical labels are closely spaced. As shown in FIG. 32, whenweak intensity activation radiation 3201 bathes closely spaced PTOLs3202 a small, statistically-sampled fraction 3203 of all the PTOLsabsorbs the activation radiation and is converted into a state 3203 thatcan be excited by the excitation radiation 3204. The emission radiation3205, 3207 from this activated and excited subset is focused to a set ofisolated, diffraction limited spots 3208 whose centers can be localizedto sub-diffractive resolution 3209 as illustrated previously in FIG. 31.After enough photons are collected to generate sufficiently resolvedimages of the PTOLs that are members of the activated and excitedsubset, the activated PTOLs are either deactivated to return to anactivatable state 3202 (as in the case of Dronpa or KFP) or arepermanently photobleached to a dark form 3213, effectively removing themfrom the system. Another cycle of weak intensity activation radiation3211 is then applied to activate a new subset 3216 of the remainingactivatable PTOLs 3212. The PTOLs in this second subset in turn can beput into the excited state 3217 by excitation 3215. The radiated light3218, 3220 is refocused by the microscope lens 3219 onto well-separateddiffractive resolution limited spots 3221. Once again, fitting of eachpeak can define the sub-diffractive locations 3222 of the PTOLs in thesecond subset. Further cycles will extract sub-diffractive locations ofother PTOLs, such as PTOL image locations 3223.

As shown in FIG. 33, multiple sub-diffractive resolution images in twospatial dimensions, x and y, of individual PTOLs in a sample can begenerated, and then the multiple images can be combined to generate asub-diffraction limited resolution image of an x-y plane of the sample.An initial image of a few discrete PTOLs emitting at a wavelength thatis imaged by imaging optics is shown in frame 3301. After a subset ofPTOLs is activated with an activation pulse of radiation having anactivation wavelength different from the wavelength of radiation that isimaged, more PTOLs are detected, as shown in frame 3302. Several suchframes are recorded until many of these initially-activated PTOLs bleachand can no longer emit, as shown in frame 3303. At this point, a newactivation pulse can convert a new subset of PTOLs into an activatedstate, and this new subset of PTOLs can emit radiation at the imagingwavelength when the newly-activated PTOLs are excited, which results inthe image of frame 3304. This cycle can be repeated to generate severalhundred or thousands of such image frames, which can be considered torepresent a 3D data stack 3305 of PTOL images, with the coordinates, xand y, on the horizontal plane and the time, t, on the vertical axis.Then all these individual image frames in the data stack can be summedto generate a total image that is equivalent to a long time exposure ofa diffraction-limited image from a microscope, as shown in frame 3306.

When activated PTOLs are sufficiently sparse in the sample, the rawsignal from each activated PTOL (e.g., the intensity of the signal onindividual pixels of a CCD detector), as shown in frame 3307, can befitted with an approximate point spread function (e.g., a Gaussian) togenerate a smoothed, fitted signal, as shown in frame 3308, and thecenter x,y coordinates of each PTOL can be determined. The location ofeach PTOL can then be rendered in a new image as a Gaussian centered atthe measured localization position, having a width defined by theuncertainty to which this location is known. This uncertainty can besignificantly less than the original radius of the original,diffraction-limited PTOL image 3307 (typically by an approximate factorof sqrt(N), where N is the number of photons detected to generated theimage of the PTOL). For example, if there were 3300 photons in thepixels of the image spot of a PTOL, the uncertainty of the fittedcentral location can be 1/20 of the size of the original diffractionlimited image of that PTOL.

Applying this process to images of all the activated PTOLs in frames3301, 3302, 3303, and 3304 leads to the corresponding narrow renderedpeaks in frames 3310, 3311, 3312, and 3313. The widths of these renderedpeaks are given by their localization uncertainty. Applied to allactivated PTOLs in all frames of the data stack 3305, this localizationprocess results in a list of coordinates for many PTOLs within thesample. Alternatively, the rendered peaks can be accumulated (e.g.,summed) to give a superresolution image 3314 of a dense set of PTOLs.The emission of any activated PTOL may persist over several frames untilit is bleached or otherwise deactivated. For such a case, animplementation of this accumulation is to identify the coordinatesacross several frames of what is likely to be a common PTOL. This set ofcoordinates can be averaged or otherwise reduced to obtain a single,more accurately localized coordinate vector of that PTOL. A comparisonof the diffraction limited image 3306 and the superresolution image 3314illustrates the higher resolution achievable by this process.

This process of serial activation of different isolated PTOL subsetsallows an effective way of localizing the positions of a dense set ofPTOLs, such that superresolution images in 1, 2, or 3 spatial dimensionscan be generated, as described in more detail herein. Furthermore, thisprocess can also be independently repeated for different species ofPTOLs within a sample, which have different activation, excitation,and/or emission wavelengths. Separate or combined superresolution imagescan then be extracted using each PTOL species. The extracted positionalinformation of two or more different PTOLs that label two differentbinding proteins can describe co-localization and relative bindingpositions on a common or closely connected target. This can be usefulfor determining which proteins are related to each other.

FIG. 34 is a flow chart of a process 3400 for creating an image of asample containing multiple relatively densely-located PTOLs. Activationradiation having an activation wavelength can be directed onto a sampleto transform a subset of PTOLs in the sample from an unactivated to anactivated state (step 3402). Excitation radiation is applied toactivated PTOLs in the sample at the excitation wavelength, andradiation that is emitted from activated and excited PTOLs and incidentonto the imaging and detecting optics is acquired and saved (step 3403).Images of a set of activated PTOLs can be acquired and saved multipletimes. For example, the controller can require that N images of a set ofactivated PTOLs are acquired, such that if N images have not yet beenacquired (step 3404) image acquisition (step 3403) is repeated. Theexcitation radiation can be applied to the sample continuously or can beswitched off between acquisitions of images.

After N images of the subset of activated PTOLs are acquired, and ifmore images are to be obtained from the sample (step 3405) anotheractivation pulse can be applied to the sample to activate another set ofPTOLs (step 3402). Excitation radiation can be applied to this other setof activated PTOLs, and radiation emitted from the activated and excitedPTOLs can be acquired and saved (step 3403). Multiple sets of PTOLs canbe activated. For example, the controller can require that M sets PTOLsbe activated, such that if M sets have not yet been activated (step3405) another activation pulse is applied (step 3403). Thus, the processof activating a set of PTOLs, exciting PTOLs within the activated set,and acquiring images from the activated and excited PTOLs can berepeated multiple times, for example, until the total pool of availablePTOLs becomes exhausted or until a desired number of images of a desirednumber of different PTOLs within a spatial area or volume is achieved.

While applying the activation and excitation radiation, the number ofiterations N between activation pulses, along with the intensity of theactivation and excitation radiation can be controlled such that the meanvolume per imaged PTOL in an individual image is generally more than theDLRV of the optical imaging system used to detect and localize theindividual PTOLs. The density of activated PTOLs that are capable ofemitting radiation is generally highest in images acquired immediatelyafter the activation pulse and generally decreases as more PTOLsphotobleach during the acquisition of the N image frames.

Furthermore, as the process 3400 progresses, and the number ofactivation pulses increases from 1 to M, PTOLs within the sample mayphotobleach, such that fewer and fewer PTOLs within the sample areavailable to be activated, excited, and imaged. Thus, in oneimplementation, the intensity and time length of individual activationpulses and the intensity and time length of excitation radiation can becontrolled, to reduce the variation in density of activated PTOLs as theprocess progresses. For example, using less excitation radiation(possibly with fewer frames N between activation pulses) can reduce thedecrease in imaged PTOLs from the first frame after an activation pulseto the Nth frame just preceding the next activation pulse. In anotherexample, the intensity of individual activation pulses can increase asthe process 3400 progresses from the first to the M^(th) activationpulse. This would reduce the decrease in the number of imaged PTOLs inthe first acquisition frame after the Mth activation pulse relative tothe number of imaged PTOLs in the first acquisition frame after thefirst activation pulse, thereby compensating for the reduction in thenumber of activable PTOLs as the sequence of activation and imageacquisition progresses. Thus, in the first example, the variation ofactivated and excitable PTOLs during an excitation sequence is reducedand in the second example the variation of activated and excitable PTOLsduring the activation sequence is reduced. The reduced variation ofactivated and excitable PTOLs allows operation, where more PTOLs can belocalized per unit time, while not exceeding the density criteria ofmore than one imaged PTOL per DLRV.

In one implementation, multiple species of PTOLs within the sample canbe activated, excited, and imaged. For example, steps of applying theactivation pulses (3402) and of exciting and imaging (3403) can includeapplying pulses of activation radiation and excitation radiation,respectively, having wavelengths corresponding to the differentactivation and excitation wavelengths of different PTOL species. Amultiplicity of detectors and/or filters can also be used in the imagingstep 3403 to image different wavelengths of radiation emitted fromdifferent PTOL species. In this manner, multiple independent data setsof images can be acquired. These independent data sets in turn can bereduced to corresponding super-resolution images of each PTOL specieswithin a sample.

If the contrast ratio between activated and inactivated PTOLs is too lowat a given initial density of target PTOLs to achieve the desired SNRand consequent localization accuracy, the contrast ratio can be improvedby irreversibly bleaching a portion of the target PTOLs until theeffective molecular density and resulting SNR is as desired. Otherautofluorescent material in the sample can also be pre-bleached usingthe excitation light without affecting the bulk of the inactivatedPTOLs. Further discrimination with respect to background might beobtained via appropriate spectral filtering, fluorescence lifetimemeasurements, or polarized excitation and/or polarization analyzeddetection.

FIG. 35 is a schematic view of a system 3500 that can be used toimplement the techniques described herein. The system 3500 is similar tothe system 1900 also includes can include a source 3502 of theactivation radiation in addition to the source 1902 of excitationradiation. The activation radiation can be coupled into the beam path ofthe excitation radiation the use of a beam splitter 3504 positionedbetween the source of excitation radiation 1902 and the lens 1904A. Asshown in FIG. 35, in some implementations, the beam paths of theexcitation radiation and the activation radiation can overlap and can bedirected to the sample 1946 by at least some of the same beam-formingoptics (e.g., galvanometer-mirrors 1928 and 1936, wavefront modulator1912, etc.). In other implementations, the excitation radiation in theactivation radiation may be provided to the sample 1946 from differentdirections. For example, the activation radiation may be provided to thesample 1946 through the detection objective 1948. In otherimplementations, the beam splitter 3504 that couples the activationradiation and the excitation radiation may be provided in a differentposition along the beam path shown in FIG. 35. For example, the beamsplitter may be located between relay lens 1940 and excitation objective1942, and the beam path for the activation radiation may includeindependent beam-forming optical elements to shape and direct theactivation beam.

The light source 3502 can be directly modulated, or modulated via ashutter 3506 placed in the beam path of the activation radiation emittedby the light source 3502. The shutter can operate to admit or preventactivation radiation from passing from the light source 3502 to thesample 1946. In one implementation, the shutter can be a mechanicalshutter that moves to selectively block the beam path. In anotherimplementation, the shutter can be a material that can be modifiedelectronically or acoustically to admit or prevent light from passing orto alter a beam path from the light source 3502. Similarly, excitationradiation that causes an activated PTOL to be transformed from ade-excited state to an excited state can also be passed from anexcitation light source 1902 through a shutter 3512 to the sample 1946.

A controller (e.g., a general or special purpose computer or processor)can control one or more optical elements of the systems 1800, 1900,3500. For example, a controller can be used to control parameters of theactivation and excitation radiation (e.g., the wavelength, intensity,polarization, and duration of pulses of various radiation beams thatreach the sample 1946 3501; and the timing of activation radiationpulses and excitation radiation pulses) during an image acquisitionsequence. Of course, the optical elements can be arranged in otherconfigurations. Data from images formed at the detector 1953 arecommunicated to a controller for storage and processing. For example,the controller can include a memory for recording or storing intensitydata as a function of position on the detector for different imageframes. The controller can also include a processor for processing thedata (e.g., a general or special purpose computer or processor), forexample, to fit the data recorded for an image of an individual PTOL todetermine a location of the PTOL to sub-diffraction limited precision,or to combine the data about the locations of multiple PTOLs that aredetermined with superresolution accuracy to generate an image of thesample based on the locations of multiple PTOLs that have been locatedwith superresolution accuracy.

Thus, in some implementations, the sample 1946 can include a denseplurality of photo transformable optical labels. The density of theoptical labels in the sample can be greater than an inverse of thediffraction limited resolution volume of the detection optics of thesystem. Activation radiation can be provided to the sample to activate astatistically sampled subset of the labels in the sample. For example,the source 3502 can generate a beam of activation light having a firstwavelength, and the activation light can be steered to the sample byoptical elements shown in system 3500.

In some implementations, the activation radiation can be provided in theform of a Bessel-like beam that is swept in a direction having acomponent orthogonal to the propagation direction of the Bessel-likebeam and having a component orthogonal to an optical axis of thedetection objective 1948. In some implementations, the activationradiation can be provided in the form of an array of incoherentBessel-like beams that are swept or dithered in a direction havingcomponents that are orthogonal both to the direction of propagation ofthe Bessel-like beams and orthogonal to an optical axis of detectionobjective 1948. In some implementations, the activation radiation can beprovided in the form of an array of coherent Bessel-like beams that areswept or dithered in a direction having components that are orthogonalboth to the direction of propagation of the Bessel-like beams andorthogonal to an optical axis of detection objective 1948. In someimplementations, the Bessel-like beams of the array can be phasecoherent with each other. In some implementations, the Bessel-like beamsin an array of beams can partially overlap with neighboring beams in thearray within the sample. In some implementations, the activationradiation can be provided in the form of a Gaussian-like beam that isswept in a direction having a component orthogonal to the propagationdirection of the Bessel-like beam and having a component orthogonal toan optical axis of the detection objective 1948. The sweeping and/ordithering of the beam(s) of activation radiation can form a thin sheetof activation radiation near a focal plane of the detection objective1948. In some implementations, the activation radiation can be providedin the form of a static thin sheet of activation radiation in a planesubstantially perpendicular to the optical axis of the detectionobjective 1948. For example, the thin sheet of activation radiation canbe formed through use of a cylindrical lens used to focus the activationradiation in one spatial direction. In some implementations, theactivation radiation is not provided in the form of a thin light sheet,but rather provided through widefield techniques. The activationradiation can be controlled such that the density of activated labels inthe subset is less than the inverse of the diffraction limitedresolution volume of the detection optics. For example, the intensity ofthe activation radiation and/or the time for which the activationradiation is provided to the sample can be controlled such that theprobability of the activation radiation activating a label convolutedwith the density of the labels in the sample is such that the resultingdensity of activated labels is less than the inverse of the diffractionlimited resolution volume of the detection optics.

Once the subset of activated labels is created, a thin sheet ofexcitation radiation can be provided to the at least some of theactivated labels in the sample to excite at least some of the activatedphoto transformable optical labels. For example, the source 1902 cangenerate a beam of excitation light having a second wavelength, and theexcitation light can be steered to the sample by optical elements shownin system 3500.

In some implementations, the excitation radiation can be provided in theform of a Bessel-like beam that is swept in a direction having acomponent orthogonal to the propagation direction of the Bessel-likebeam and having a component orthogonal to an optical axis of thedetection objective 1948. In some implementations, the excitationradiation can be provided in the form of an array of Bessel-like beamsthat are swept or dithered in a direction having components that areorthogonal both to the direction of propagation of the Bessel-like beamsand orthogonal to an optical axis of detection objective 1948. In someimplementations, the Bessel-like beams can be phase coherent with eachother. In some implementations, Bessel-like beams in an array of beamscan partially overlap with neighboring beams in the array within thesample.

In some implementations, the excitation radiation can be provided in theform of a Gaussian-like beam that is swept in a direction having acomponent orthogonal to the propagation direction of the Bessel-likebeam and having a component orthogonal to an optical axis of thedetection objective 1948. The sweeping and/or dithering of the beam(s)of excitation radiation can form a thin sheet of excitation radiationnear a focal plane of the detection objective 1948. In someimplementations, the excitation radiation can be provided in the form ofa static thin sheet of excitation radiation in a plane substantiallyperpendicular to the optical axis of the detection objective 1948. Forexample, the thin sheet of excitation radiation can be formed throughuse of a cylindrical lens used to focus the excitation radiation in onespatial direction.

Radiation emitted from the activated and excited labels is imaged byimaging optics, including the detection objective 1948, onto a detector1953. The detection objective has an axis along a direction that issubstantially perpendicular to the sheet of excitation radiation.Locations of labels from which radiation is detected can be determinedwith super resolution accuracy by one or more processors or computingdevices based on the detected radiation. The process of activating astatistical subset of transformable labels, exciting the activatedlabels, and detecting light from the activated and excited labels can berepeated, where different subsets of transformable labels are activatedduring different rounds of activation. Finally, asub-diffraction-limited image of the sample can be generated by one ormore processors of a computing system based on the determined locationsof the labels.

Other planes of the sample 1946 can be imaged by moving the activationradiation and the excitation radiation and the focal plane of thedetection objective 1948 to different positions within the sample. Forexample, in one implementation, the sample can be mounted on a movablestage 3506 that is configured to change the position of the sample withrespect to the focal plane of the detection objective 1948. In anotherimplementation, the activation radiation and the excitation radiationcan be steered to different planes along the axial direction of thedetection objective by the beam-forming optics of the system 3500 (e.g.,by galvanometer-mirror 1928). When the activation and excitationradiation beams are steered to different positions within the sample,the focal plane of the detection objective can be changedcorrespondingly, such that committing optical labels from the newlypositioned plane of excitation radiation can be imaged effectively bythe detection objective 1948. When optical labels in different planes ofthe sample are activated, excited, and imaged, the locations of theoptical labels in the different planes can be combined to generate athree-dimensional image of the sample.

Implementations of the various techniques described herein may beimplemented in digital electronic circuitry, or in computer hardware,firmware, software, or in combinations of them. Implementations mayimplemented as a computer program product, i.e., a computer programtangibly embodied in an information carrier, e.g., in a machine-readablestorage device or in a propagated signal, for execution by, or tocontrol the operation of, data processing apparatus, e.g., aprogrammable processor, a computer, or multiple computers. A computerprogram, such as the computer program(s) described above, can be writtenin any form of programming language, including compiled or interpretedlanguages, and can be deployed in any form, including as a stand-aloneprogram or as a module, component, subroutine, or other unit suitablefor use in a computing environment. A computer program can be deployedto be executed on one computer or on multiple computers at one site ordistributed across multiple sites and interconnected by a communicationnetwork.

Method steps may be performed by one or more programmable processorsexecuting a computer program to perform functions by operating on inputdata and generating output. Method steps also may be performed by, andan apparatus may be implemented as, special purpose logic circuitry,e.g., an FPGA (field programmable gate array) or an ASIC(application-specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read-only memory ora random access memory or both. Elements of a computer may include atleast one processor for executing instructions and one or more memorydevices for storing instructions and data. Generally, a computer alsomay include, or be operatively coupled to receive data from or transferdata to, or both, one or more mass storage devices for storing data,e.g., magnetic, magneto-optical disks, or optical disks. Informationcarriers suitable for embodying computer program instructions and datainclude all forms of non-volatile memory, including by way of examplesemiconductor memory devices, e.g., EPROM, EEPROM, and flash memorydevices; magnetic disks, e.g., internal hard disks or removable disks;magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor andthe memory may be supplemented by, or incorporated in special purposelogic circuitry.

To provide for interaction with a user, implementations may beimplemented on a computer having a display device, e.g., a cathode raytube (CRT) or liquid crystal display (LCD) monitor, for displayinginformation to the user and a keyboard and a pointing device, e.g., amouse or a trackball, by which the user can provide input to thecomputer. Other kinds of devices can be used to provide for interactionwith a user as well; for example, feedback provided to the user can beany form of sensory feedback, e.g., visual feedback, auditory feedback,or tactile feedback; and input from the user can be received in anyform, including acoustic, speech, or tactile input.

While certain features of the described implementations have beenillustrated as described herein, many modifications, substitutions,changes and equivalents will now occur to those skilled in the art. Itis, therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the true spiritof the implementations.

What is claimed is:
 1. An apparatus comprising: a light sourceconfigured for generating a coherent light beam having a wavelength, λ;beam-forming optics configured for receiving the generated light beamand for generating a plurality of substantially parallel phase-coherentBessel-like beams directed into a sample in a first direction, whereinthe Bessel-like beams have a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.95; a lightdetector; imaging optics configured for receiving light from a positionwithin the sample that is illuminated by the Bessel-like beams and forimaging the received light onto the detector, the imaging opticsincluding a detection objective having an axis oriented in a seconddirection that is non-parallel to the first direction, wherein thedetector is configured for detecting light received by the imagingoptics; and a processor configured to generate an image of the samplebased on the detected light.
 2. The apparatus of claim 1, wherein theplurality of Bessel-like beams are spaced from their neighboring beamsby distances close enough that the side lobes of adjacent beamsinterfere with one another.
 3. The apparatus of claim 2, wherein atleast one of the side lobes of each beam substantially overlaps with oneof the side lobes of an adjacent beam, and the overlapping side lobeshave substantially the same phase.
 4. The apparatus of claim 1, whereinthe plurality of Bessel-like beams are spaced from their neighboringbeams by distances large enough that the side lobes of adjacent beams donot substantially interfere with one another.
 5. The apparatus of claim1, wherein the plurality of Bessel-like beams are arranged substantiallyin a plane in the sample.
 6. The apparatus of claim 3, wherein theplurality of Bessel-like beams partially overlap with neighboringBessel-like beams in the sample and wherein the beam-forming opticsinclude a wavefront modulating element (WME) configured for controllingthe relative spacing of the different Bessel-like beams in the sample,wherein the relative spacing of the different Bessel-like beams is suchthat destructive interference between neighboring Bessel-like beamsoccurs at positions that are not in the plane.
 7. The apparatus of claim1, further comprising: a diffractive optical element (DOE) configured togenerate a plurality of light beams from the light beam generated by thelight source; and wherein the beam-forming optics are configured forreceiving the plurality of light beams and generating the plurality ofBessel-like beams in the sample.
 8. The apparatus of claim 1, whereinthe beam forming optics include a wavefront modulating element (WME)positioned to be optically conjugate to the sample and configured toreceive the light beam and to generate the plurality of Bessel-likebeams in the sample.
 9. The apparatus of claim 6, wherein the WMEincludes a spatial light modulator (SLM).
 10. The apparatus of claim 7,wherein the SLM includes a binary spatial light modulator (SLM).
 11. Theapparatus of claim 7, wherein the SLM is configured to control therelative phrases of the individual Bessel-like beams.
 12. The apparatusof claim 1, further comprising beam scanning optics configured forscanning the Bessel-like beams within the sample in a second directionhaving a component perpendicular to the first direction.
 13. Theapparatus of claim 12, wherein the processor is configured to generatethe image based on the detected light received from different positionsto which the Bessel beams are scanned within the sample.
 14. Theapparatus of claim 12, wherein the beam scanning optics are furtherconfigured for scanning the Bessel-like beams within the sample in athird direction having a component perpendicular to both the first andsecond directions.
 15. The apparatus of claim 12, wherein the pluralityof Bessel-like beams are arranged in the plane in a pattern having aspatial period, Λ, and wherein the beam scanning optics are configuredto scan the pattern in the plane in N discrete steps, the steps having alength of Λ/N, and further comprising: a processor configured togenerate N images from the detected light, each n image, for n=1 to N,being based on detected light due to excitation of the sample by then^(th) excitation pattern and further configured generate a final imageof the sample through a linear combination of the N individual images.16. The apparatus of claim 15, wherein generating the final image of thesample through a linear combination of the N individual images, includescombining the individual images according to$I_{final} = \left| {\sum\limits_{n = 1}^{N}\;{I_{n}{\exp\left( {2\pi\;{in}\text{/}N} \right)}}} \middle| . \right.$17. The apparatus of claim 1, wherein the detected light is generatedthough a non-linear signal generation process.
 18. The apparatus ofclaim 17, wherein the detected light has a wavelength of λ/2.
 19. Theapparatus of claim 1, wherein the Bessel-like beams have a ratio of aRayleigh length, z_(R) to a minimum beam waist, w_(o), of more than2πw_(o)/λ and less than 100πw_(o)/λ.
 20. The apparatus of claim 1,wherein the Bessel-like beams have a non-zero ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.90.21. The apparatus of claim 1, wherein the Bessel-like beams have aminimum numerical aperture greater than zero and a ratio of energy in afirst side of the beam to energy in the central lobe of the beam of lessthan 0.5.
 22. The apparatus of claim 1, wherein the plurality ofBessel-like beams partially are arranged substantially in a plane andoverlap with neighboring Bessel-like beams in the sample.
 23. Theapparatus of claim 1, further comprising an annular mask in a path ofthe light beam configured to generate an annular ring of light fromwhich the Bessel-like beam is formed.
 24. The apparatus of claim 1,wherein the plurality of Bessel-like beams are arranged substantially ina plane in the sample, and further comprising a dithering opticalelement configured to dither the positions of the plurality ofBessel-like beams within the plane at a dither frequency.
 25. Theapparatus of claim 24, wherein the dithering optical element isconfigured to dither the Bessel-like beams over a distance, such that atime-averaged intensity of the light in the plane, averaged over theinverse of at least one dither frequency is substantially constant overa region within the plane that spans at least two of the Bessel-likebeams.
 26. The apparatus of claim 25, wherein the plurality ofBessel-like beams partially overlap with neighboring Bessel-like beamsin the sample and wherein the beam-forming optics include a wavefrontmodulating element (WME) configured for controlling the relative spacingof the different Bessel-like beams in the sample, wherein the relativespacing of the different Bessel-like beams is such that destructiveinterference between neighboring Bessel-like beams occurs at positionsthat are not in the plane.
 27. The apparatus of claim 26, wherein theBessel-like beams have a ratio of a Rayleigh length, z_(R) to a minimumbeam waist, w_(o), of more than 2πw_(o)/λ and less than 100πw_(o)/λ. 28.The apparatus of claim 26, wherein the Bessel-like beams have a non-zeroratio of a minimum numerical aperture to a maximum numerical aperture ofless than 0.95.
 29. The apparatus of claim 26, wherein the Bessel-likebeams have a non-zero ratio of a minimum numerical aperture to a maximumnumerical aperture of less than 0.90.
 30. The apparatus of claim 26,wherein the Bessel-like beams have a minimum numerical aperture greaterthan zero and a ratio of energy in a first side of the beam to energy inthe central lobe of the beam of less than 0.5.
 31. A method comprising:generating a coherent light beam having a wavelength, λ; generating fromthe coherent beam a plurality of substantially parallel phase-coherentBessel-like beams directed into a sample in a first direction, whereinthe Bessel-like beams have a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.95; imaging,with imaging optics, light received from a position within the samplethat is illuminated by the Bessel-like beams onto detector, the imagingoptics including a detection objective having an axis oriented in asecond direction that is non-parallel to the first direction; andgenerating an image of the sample based on the detected light.
 32. Themethod of claim 31, wherein the plurality of Bessel-like beams arespaced from their neighboring beams by distances close enough that theside lobes of adjacent beams interfere with one another.
 33. The methodof claim 31, wherein the plurality of Bessel-like beams are spaced fromtheir neighboring beams by distances large enough that the side lobes ofadjacent beams do not substantially interfere with one another.
 34. Themethod of claim 31, wherein the plurality of Bessel-like beams arearranged substantially in a plane in the sample.
 35. The method of claim32, further controlling the relative spacing of the differentBessel-like beams in the sample, wherein the relative spacing of thedifferent Bessel-like beams is such that destructive interferencebetween neighboring Bessel-like beams occurs at positions that are notin the plane.
 36. The method of claim 35, wherein controlling therelative spacing of the Bessel-like beams includes reflecting theBessel-like beams off a wavefront modulating element (WME) andcontrolling the WME to control the relative phrases.
 37. The method ofclaim 36, wherein the WME includes a spatial light modulator (SLM). 38.The method of claim 31, further comprising scanning the Bessel-likebeams within the sample in a direction having a component perpendicularto the first direction.
 39. The method of claim 38, further comprisinggenerating the image based on the detected light received from differentpositions to which the Bessel beams are scanned within the sample. 40.The method of claim 31, wherein the plurality of Bessel-like beams areequally spaced from neighboring beams in the plane in a pattern having aspatial period, Λ, and further comprising: scanning the pattern in theplane in N discrete steps, the steps having a length of Λ/N; andgenerating N images from the detected light, each n image, for n=1 to N,being based on detected light due to excitation of the sample by then^(th) excitation pattern and further configured generate a final imageof the sample through a linear combination of the N individual images.41. The method of claim 40, further comprising generating the finalimage of the sample through a linear combination of the N individualimages by combining the individual images according to$I_{final} = \left| {\sum\limits_{n = 1}^{N}\;{I_{n}{\exp\left( {2\pi\;{in}\text{/}N} \right)}}} \middle| . \right.$42. The method of claim 31, wherein the detected light is generatedthough a non-linear signal generation process.
 43. The method of claim42, wherein the detected light has a wavelength of λ/2.
 44. The methodof claim 31, wherein the Bessel-like beams have a ratio of a Rayleighlength, z_(R) to a minimum beam waist, w_(o), of more than 2πw_(o)/λ andless than 100πw_(o)/λ.
 45. The method of claim 31, wherein theBessel-like beams have a non-zero ratio of a minimum numerical apertureto a maximum numerical aperture of less than 0.90.
 46. The method ofclaim 31, wherein the Bessel-like beams have a minimum numericalaperture greater than zero and a ratio of energy in a first side of thebeam to energy in the central lobe of the beam of less than 0.5.
 47. Themethod of claim 31, wherein the plurality of Bessel-like beams arearranged substantially in a plane in the sample, and further comprising:dithering the positions of the plurality of Bessel-like beams within theplane at a dither frequency.
 48. The method of claim 47, whereindithering the beams includes dithering the Bessel-like beams over adistance, such that a time-averaged intensity of the light in the plane,averaged over the inverse of the dither frequency is substantiallyconstant over a region within the plane that spans at least two of theBessel-like beams.
 49. The method of claim 48, further comprisingcontrolling the relative spacing of the different Bessel-like beams,wherein the relative spacing of the different Bessel-like beams is suchthat destructive interference between neighboring Bessel-like beamsoccurs at positions that are not in the plane.
 50. The method of claim49, wherein the Bessel-like beams have a ratio of a Rayleigh length,z_(R) to a minimum beam waist, w_(o), of more than 2πw_(o)/λ and lessthan 100πw_(o)/λ.
 51. The method of claim 49, wherein the Bessel-likebeams have a non-zero ratio of a minimum numerical aperture to a maximumnumerical aperture of less than 0.95.
 52. The method of claim 49,wherein the Bessel-like beams have a non-zero ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.90.53. The method of claim 49, wherein the Bessel-like beams have a minimumnumerical aperture greater than zero and a ratio of energy in a firstside of the beam to energy in the central lobe of the beam of less than0.5.
 54. A method comprising: (a) providing activation radiation to asample that includes phototransformable optical labels (“PTOLs”) toactivate a statistically sampled subset of the PTOLs in the sample,wherein the PTOLs are distributed in at least a portion of the samplewith a density greater than an inverse of the diffraction-limitedresolution volume (“DLRV”) of imaging optics; (b) providing a sheet ofexcitation radiation into the sample to excite at least some of theactivated PTOLs in a plane defined by the sheet, wherein providing theexcitation radiation sheet includes providing at least one Bessel-likebeam of excitation radiation into the sample and wherein the at leastone Bessel-like beam has a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.95; (c)detecting with the imaging optics radiation emitted from activated andexcited PTOLs within the first subset of PTOLs, wherein the imagingoptics include an objective lens having an axis along a direction thatis substantially perpendicular to the plane; (d) determining locationswithin the sample of the PTOLs from which radiation is detected withsuperresolution accuracy; (e) controlling the activation radiation suchthat the density of activated PTOLs in the subset is less than theinverse of the (“DLRV”) of the imaging optics; (f) repeating (a)-(e) todetermine location of more PTOLs within the sample; and (g) generating asub-diffraction-limited image of the sample based on the determinedlocations of the PTOLs.
 55. The method of claim 54, wherein the sheet ofexcitation radiation has a maximum thickness of about 3 micrometers overa distance of about 6 micrometers along a propagation direction of thesheet in a region of the minimum thickness position of the sheet. 56.The method of claim 54, wherein the activation radiation is provided ina sheet having a maximum thickness of about 3 micrometers over adistance of about 6 micrometers along a propagation direction of theactivation radiation sheet in a region of the minimum thickness positionof the sheet, and wherein the activation radiation sheet issubstantially parallel to, and at least partially overlaps, theexcitation radiation sheet.
 57. The method of claim 56, whereinproviding the activation radiation sheet includes providing a pluralityof Bessel-like beams arranged substantially in the plane.
 58. The methodof claim 54, wherein providing the excitation radiation sheet includes aplurality of Bessel-like beams arranged substantially in the plane. 59.The method of claim 54, wherein providing the sheet of excitationradiation includes providing a Gaussian beam of excitation radiation andsweeping the Gaussian beam in a direction perpendicular to a propagationdirection of the beam.
 60. The method of claim 54, wherein providing thesheet of excitation radiation includes focusing a Gaussian beam ofexcitation radiation with a cylindrical lens to create the excitationradiation sheet in the sample.
 61. The method of claim 54, whereinproviding the sheet of excitation radiation includes providing aBessel-like beam of excitation radiation and sweeping the Bessel-likebeam in a direction perpendicular to a propagation direction of thebeam.
 62. The method of claim 54, providing the sheet of activationradiation includes providing a Bessel-like beam of activation radiationand sweeping the Bessel-like beam in a direction perpendicular to apropagation direction of the beam.
 63. The method of claim 54, furthercomprising: (h) changing the position of the plane with respect to thesample; and (i) repeating (a)-(e), wherein generating the image includesgenerating the image based on the determined locations of the PTOL fordifferent positions of the plane with respect to the sample.
 64. Themethod of claim 63, wherein changing the position of the plane withrespect to the sample includes translating the sample.
 65. The method ofclaim 63, wherein changing the position of the plane with respect to thesample includes translating the plane.
 66. The method of claim 54,wherein the imaging optics includes an objective lens and whereinproviding the activation radiation includes transmitting the activationradiation through the objective lens.
 67. The method of claim 54,wherein the PTOLs include fluorescent proteins.
 68. The method of claim54, further comprising deactivating at least some of the activated PTOLsafter (e) and before (f).
 69. The method of claim 68, wherein thedeactivating includes providing sufficient excitation radiation tophotobleach PTOLs in the first subset of PTOLs.
 70. The method of claim54, wherein the activation radiation has an activation wavelength andwherein the excitation radiation has an excitation wavelength that islonger than the activation wavelength.
 71. The method of claim 54,wherein providing the activation radiation to the sample includesactivating PTOLs in the first subset through a multi-photon absorptionprocess.
 72. The method of claim 54, wherein providing the excitationradiation to the sample includes exciting PTOLs in the first subset ofPTOLs through a multi-photon absorption process.
 73. The method of claim54, further comprising sweeping the at least one Bessel-like beam in adirection perpendicular to a propagation direction of the beam.
 74. Themethod of claim 54, wherein the sheet of excitation radiation includes aplurality of Bessel-like beams arranged substantially in a plane,wherein the plurality of Bessel-like beams partially overlap withneighboring Bessel-like beams in the sample, and wherein the pluralityof Bessel-like beams are phase coherent with each other.
 75. The methodof claim 74, wherein the plurality of Bessel-like beams are spaced fromtheir neighboring beams by distances such that destructive interferencebetween neighboring Bessel-like beams occurs at positions that are notin the plane.
 76. The method of claim 74, further comprising controllingrelative phases of the different Bessel-like beams.
 77. The method ofclaim 76, wherein the plurality of Bessel-like beams are spaced fromtheir neighboring beams by distances that are less than a diameter of afirst side lobe of the Bessel-like beams and wherein controlling therelative phrase of the different Bessel-like beams includes controllingthe relative phases such that destructive interference betweenneighboring Bessel-like beams occurs at positions that are not in theplane.
 78. The method of claim 76, wherein controlling the relativephrases of the Bessel-like beams includes reflecting the Bessel-likebeams off a wavefront modulating element (WME) and controlling the WMEto control the relative phrases.
 79. The method of claim 78, wherein theWME includes a spatial light modulator (SLM).
 80. The method of claim79, wherein the plurality of Bessel-like beams are equally spaced fromneighboring beams in the plane in a pattern having a spatial period, Λ,and further comprising: scanning the pattern in the plane in N discretesteps, the steps having a length of Λ/N; and generating N images fromthe detected light, each n image, for n=1 to N, being based on detectedlight due to excitation of the sample by the n^(th) excitation patternand further configured generate a final image of the sample through alinear combination of the N individual images.
 81. The method of claim80, further comprising generating the final image of the sample througha linear combination of the N individual images by combining theindividual images according to$I_{final} = \left| {\sum\limits_{n = 1}^{N}\;{I_{n}{\exp\left( {2\pi\;{in}\text{/}N} \right)}}} \middle| . \right.$82. The method of claim 54, wherein the at least one Bessel-like beamhas a ratio of a Rayleigh length, z_(R) to a minimum beam waist, w_(o),of more than 2πw_(o)/λ and less than 100πw_(o)/λ.
 83. The method ofclaim 54, wherein the at least one Bessel-like beam has a non-zero ratioof a minimum numerical aperture to a maximum numerical aperture of lessthan 0.90.
 84. The method of claim 54, wherein the at least oneBessel-like beam has a minimum numerical aperture greater than zero anda ratio of energy in a first side of the beam to energy in the centrallobe of the beam of less than 0.5.
 85. The method of claim 54, furthercomprising: dithering the position(s) of the at least one Bessel-likebeam within the plane at a dither frequency.
 86. The method of claim 85,wherein dithering the at least one Bessel-like beam includes ditheringthe at least one Bessel-like beam over a distance, such that atime-averaged intensity of the light in the plane, averaged over theinverse of at least one dither frequency is substantially constant overa region over which the at least one Bessel-like beam is dithered. 87.The method of claim 86, further comprising controlling the relativephrase of the different Bessel-like beams such that destructiveinterference between neighboring Bessel-like beams occurs at positionsthat are not in the plane.
 88. The method of claim 54, wherein thedetected light is generated though a non-linear signal generationprocess.
 89. The method of claim 88, wherein the detected light has awavelength of that is half the wavelength of the excitation radiation.90. An apparatus comprising: a first light source for generating a firstlight beam having a wavelength, λ₁; first beam-forming optics configuredfor receiving the generated light beam and for generating activationradiation to a sample that includes phototransformable optical labels(“PTOLs”) to activate a statistically sampled subset of the PTOLs in thesample, wherein the PTOLs are distributed in at least a portion of thesample with a density greater than an inverse of the diffraction-limitedresolution volume (“DLRV”) of imaging optics; a second light source forgenerating a second light beam having a wavelength, λ₂; secondbeam-forming optics configured for receiving the second generated beamand providing a sheet of excitation radiation to the sample to excite atleast some of the activated PTOLs, wherein the sheet of excitationradiation includes at least one Bessel-like beam of excitation radiationand wherein the at least one Bessel-like beam has a non-zero ratio of aminimum numerical aperture to a maximum numerical aperture of less than0.95; a detector configured for detecting radiation emitted fromactivated and excited PTOLs within the first subset of PTOLs; imagingoptics configured for receiving radiation emitted from activated andexcited PTOLs and for imaging the received light onto the detector, theimaging optics including a detection objective having an axis orientedin a direction that is substantially perpendicular to the plane; acontroller configured for controlling the activation radiation such thatthe density of activated PTOLs in the subset is less than the inverse ofthe (“DLRV”) of the imaging optics; one or more processors of acomputing system configured for determining, with superresolutionaccuracy, locations within the sample of the PTOLs from which radiationis detected; and one or more processors of the computing systemconfigured for generating a sub-diffraction-limited image of the samplebased on the determined locations of the PTOLs.
 91. The apparatus ofclaim 90, wherein the sheet of excitation radiation has a maximumthickness of about 3 micrometers over a distance of about 6 micrometersalong a propagation direction of the sheet in a region of the minimumthickness position of the sheet.
 92. The apparatus of claim 90, whereinthe first light source and the first beam-forming optics are configuredfor providing the activation radiation to the sample in a sheet having amaximum thickness of about 3 micrometers over a distance of about 6micrometers along a propagation direction of the activation radiationsheet in a region of the minimum thickness position of the sheet whereinthe activation radiation sheet has a maximum thickness of about 3micrometers over a distance of about 6 micrometers along a propagationdirection of the sheet in a region of the minimum thickness position ofthe sheet, and wherein the activation radiation sheet is substantiallyparallel to, and at least partially overlaps, the excitation radiationsheet.
 93. The apparatus of claim 90, wherein providing the activationradiation sheet includes a providing a plurality of Bessel-like beamsarranged substantially in the plane.
 94. The apparatus of claim 90,wherein providing the sheet of excitation radiation includes providing aGaussian beam of excitation radiation and sweeping the Gaussian beam ina direction perpendicular to a propagation direction of the beam. 95.The apparatus of claim 90, wherein the second beam-forming opticsinclude a cylindrical lens and wherein providing the sheet of excitationradiation includes focusing a Gaussian beam of excitation radiation withthe cylindrical lens to create the excitation radiation sheet in thesample.
 96. The apparatus of claim 90, wherein the sheet includes aplurality of Bessel-like beams arranged substantially in the plane. 97.The apparatus of claim 90, further comprising a movable stage configuredfor supporting the sample and for moving the sample in a directionhaving a component parallel to the axis of the detection objective. 98.The apparatus of claim 90, wherein the imaging optics are configured tomove a focal plane of the imaging optics in the sample in a directionalong an axial direction of the detection objective.
 99. The apparatusof claim 90, wherein the first beam-forming optics are configured toprovide the activation radiation through the detection objective. 100.The apparatus of claim 90, wherein the PTOLs include fluorescentproteins.
 101. The apparatus of claim 90, wherein the λ₁ is shorter thanthe λ₂.
 102. The apparatus of claim 90, wherein providing the excitationradiation sheet includes sweeping the at least one Bessel-like beam in adirection perpendicular to a propagation direction of the beam.
 103. Theapparatus of claim 90, wherein the sheet of excitation radiationincludes a plurality of Bessel-like beams arranged substantially in aplane, wherein the plurality of Bessel-like beams partially overlap withneighboring Bessel-like beams in the sample, and wherein the pluralityof Bessel-like beams are phase coherent with each other.
 104. Theapparatus of claim 103, wherein the plurality of Bessel-like beams arespaced from their neighboring beams by distances that are less than adiameter of a first side lobe of the Bessel-like beams.
 105. Theapparatus of claim 103, wherein the second beam-forming optics include aphase controller configured for controlling the relative phases of thedifferent Bessel-like beams.
 106. The apparatus of claim 103, whereinthe plurality of Bessel-like beams are spaced from their neighboringbeams by distances that are less than a diameter of a first side lobe ofthe Bessel-like beams and wherein the phase controller is configured forcontrolling the relative phases such that destructive interferencebetween neighboring Bessel-like beams occurs at positions that are notin the plane.
 107. The apparatus of claim 106, wherein the destructiveinterference between neighboring Bessel-like beams occurs at positionsthat are not in the plane but that within a distance of the plane thatis less than the diameter of first side lobes of the Bessel-like beams.108. The apparatus of claim 105, wherein the phase controller includes areflective wavefront modulating element (WME) configured for reflectingthe Bessel-like beams and for controlling relative phrases of thedifferent Bessel-like beams.
 109. The apparatus of claim 108, whereinthe WME includes a spatial light modulator (SLM).
 110. The apparatus ofclaim 103, wherein the plurality of Bessel-like beams are equally spacedfrom neighboring beams in the plane in a pattern having a spatialperiod, Λ, and wherein the second beam-scanning optics are configuredfor scanning the pattern in the plane in N discrete steps, the stepshaving a length of Λ/N; and wherein the one or more processors of thecomputing system are configured for generating N images from thedetected light, each n image, for n=1 to N, being based on detectedlight due to excitation of the sample by the n^(th) excitation patternand further configured generate a final image of the sample through alinear combination of the N individual images.
 111. The apparatus ofclaim 110, wherein generating the final image of the sample through alinear combination of the N individual images includes combining theindividual images according to$I_{final} = \left| {\sum\limits_{n = 1}^{N}\;{I_{n}{\exp\left( {2\pi\;{in}\text{/}N} \right)}}} \middle| . \right.$112. The apparatus of claim 90, wherein the at least one Bessel-likebeam has a ratio of a Rayleigh length, z_(R) to a minimum beam waist,w_(o), of more than 2πw_(o)/λ and less than 100πw_(o)/λ.
 113. Theapparatus of claim 90, wherein the at least one Bessel-like beam has anon-zero ratio of a minimum numerical aperture to a maximum numericalaperture of less than 0.95.
 114. The apparatus of claim 90, wherein theat least one Bessel-like beam has a non-zero ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.90.115. The apparatus of claim 90, wherein the at least one Bessel-likebeam has a minimum numerical aperture greater than zero and a ratio ofenergy in a first side of the beam to energy in the central lobe of thebeam of less than 0.5.
 116. The apparatus of claim 90, whereinmanipulating the at least one Bessel-like beam includes dithering theposition(s) of the at least one Bessel-like beam within the plane at adither frequency.
 117. The apparatus of claim 116, wherein dithering theat least one Bessel-like beam includes dithering the at least oneBessel-like beam over a distance, such that a time-averaged intensity ofthe light in the plane, averaged over the inverse of at least one ditherfrequency is substantially constant over a region over which the atleast one Bessel-like beam is dithered.
 118. The apparatus of claim 90,wherein the detected light has a wavelength that is shorter than thewavelength of the excitation radiation.
 119. The apparatus of claim 118,wherein the detected light has a wavelength of that is half thewavelength of the excitation radiation.